Free online graphing calculator - graph functions, conics, and inequalities interactively.Solution. Already the absolute value expression is isolated, therefore assume the absolute symbols and solve. | x + 2 | = 7 → x + 2 = 7. Subtract 2 from both sides. x + 2 - 2 = 7 -2. x = 5. Multiply 7 by -1 to solve for the negative version of the equation. x + 2 = -1 (7) → x + 2 = -7. Subtract by 2 on both sides.Transcript. Absolute value is a fundamental math concept that measures the distance of a number from zero, regardless of its sign. It's always a positive value, as it represents the magnitude of a number without considering its direction. This concept is useful in real-world applications, such as calculating distances and comparing heights.With the absolute value calculator, the function abs can calculate the absolute value online of a number. To calculate the absolute value of a number, just enter the number and to apply the function abs. Thus, for calculating the absolute value of the number -5, you must enter abs ( − 5 - 5) or directly -5, if the button abs already appears ...The absolute value of 4-7i to the square root of. verified. Verified answer. 4. The distance between a + 7i and -8 + 4i is Square root of 130 units The positive value of a is . star. 4.8/5. heart. 24. verified. Verified answer. Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is JenniferAnswer: Option 1 is correct. Explanation: We have been given with the function 4 -7i. To find the absolute value means to find the modulus of the function. And modulus of the function is. Here we have a=4 and b= -7 so substituting the values in the formula we will get. Hence, Option 1 is correct. Option 2 is incorrect because we do not consider ...The absolute value is the distance between a number and zero. The distance between and is . Step 3.3.2.3. The final answer is . Step 3.4. The absolute value can be graphed using the points around the vertex. Step 4 ...The number doctors look at is called your absolute neutrophil count (ANC). For a healthy person, the normal range for an ANC is between 2,500 and 6,000. The ANC is found by multiplying the WBC count by the percent of neutrophils in the blood. For instance, if the WBC count is 8,000 and 50% of the WBCs are neutrophils, the ANC is 4,000 (8,000 × ...The absolute value function is commonly used to measure distances between points. Applied problems, such as ranges of possible values, can also be solved using the absolute value function. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.Absolute-value equations can be fairly simple when they contain only one absolute-value expression, and if that expression is linear. But these equations can have many more than just one expression in absolute-value bars, and the bars may contain expressions more complicated than mere straight lines. We'll start with a quadratic expression as ...The absolute value is denoted as |x| or abs (x), and functions such that: |x| = x. and. |-x| = x. For example, the numbers 2 and -2 have a distance of 2 from 0, so their absolute …Free Complex Numbers Calculator - Simplify complex expressions using algebraic rules step-by-stepBut, presumably, the most important natural logarithm is the one that calculates the value of a number between 1 and e, which turns out to be the number 2. Using the natural log calculator, we get. ln 2 = 0.6931. It turns out that ln 2 is also equal to the alternating sum of reciprocals of all natural numbers: ln 2 = 1 - 1/2 + 1/3 - 1/4 + 1 ...The complex number is, We know that, The absolute value of a complex number x + iy, is defined as the distance between the origin (0, 0) and the point (x, y) in the complex plane. Its value is calculated by, Now, by using the above formula the absolute value of the complex number is, ⇒ =. To learn more about absolute value visit:In algebra, an absolute value (also called a valuation, magnitude, or norm, [1] although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping |x| from D to the ...Understanding Absolute Value. Recall that in its basic form f (x) = |x|, f ( x) = | x |, the absolute value function is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value ...Absolute-Value Detection is a popular algorithm used for sorting spiking signals, and the 4-bit Absolute-Value Detector is a fundamental circuit in the spike-sorting field. This paper presents ...Enter Double Number = -34556.8765 Enter Float Number = -2345.239f Actual Double Number = -34556.876500 Absolute Double Number = 34556.876500 Actual Float Number = -2345.239 Absolute Float Number = 2345.239. This c example uses the labs function to find the absolute value of a long number.To use the absolute value calculator, enter the number you'd like to find the absolute value for in the Input box. Then, click the Compute Absolute Value button. We'll return the number's absolute value in the Absolute Value box. Next, try our other calculators and tools. PK started DQYDJ in 2009 to research and discuss finance and investing ...Shift absolute value graphs Get 3 of 4 questions to level up! Scale & reflect absolute value graphs Get 3 of 4 questions to level up! Graph absolute value functions Get 3 of 4 questions to level up! Quiz 1. Level up on the above skills and collect up to 240 Mastery points Start quiz. Piecewise functions.The absolute value of a real number is the distance of the number from 0 0 on a number line. The absolute value of x x is written as \left|x\right|. ∣x∣. For example, \left|5\right| = \left|-5\right| = 5. ∣5∣ = ∣−5∣ = 5. This is a special case of the magnitude of a complex number.3. I would guess it is your first option. A usual terminology in calculus is about absolute and relative (or local) maxima and minima. The absolute maximum would be then max{f(x): x ∈ [−2, 4]} max { f ( x): x ∈ [ − 2, 4] }. The phrase "absolute maximum value " probably has to do with the fact that when looking at extrema of functions ...The absolute value of any integer, whether positive or negative, will be the real numbers, regardless of which sign it has." Here, The given complex number is -4 - sqrt 2i. The absolute value of a complex number is. Here a = -4, b = sqrt (2) So, absolute value of the complex number is. Hence, the absolute value is sqrt (18). Solution. First, set the expression inside the absolute value bars equal to zero and solve for x. Note that x − 2 = 0 at x = 2. This is the “critical value” for this expression. Draw a real line and mark this critical value of x on the line. Place the expression x − 2 below the line at its left end. Absolute value. In this section you'll learn how to the find the absolute value of integers. In this pattern you can see that 4 - 5 is equal to a negative number. A negative number is a number that is less than zero (in this case -1). A negative number is always less than zero, 0. We can study this in a diagram by using two examples: 0 - 4 = -4 ... The modulus or magnitude of a complex number ( denoted by ∣z∣ ), is the distance between the origin and that number. If the z = a+ bi is a complex number than the modulus is. ∣z∣ = a2 + b2. Example 01: Find the modulus of z = 6 + 3i. In this example a = 6 and b = 3, so the modulus is: ∣z∣ = a2 +b2 = 62 +32 = = 36 + 9 = 45 = = 9 ⋅5 ...Yes. In general, to solve an equation with an absolute value: Perform inverse operations until the absolute value stands by itself on one side of the equation--the equation should be of the form| expression | = c. If c is negative, the equation has no solution . Separate into two equations: expression = c or expression = -c Note that "or ...Algebra Properties of Real Numbers Additive Inverses and Absolute Values. 2 Answers Wataru Nov 11, 2014 Remember that the absolute value sign is a negative sign eraser, so we have: #{(|-10|=10),(|10|=10):}# I hope that this was helpful. Answer link. Firelight Nov 11 ...Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve an equation such as 8 = | 2 x − 6 |, 8 = | 2 x − 6 |, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8. This leads to two different equations we can solve independently.The absolute value or modulus of a number is its non-negative value or distance from zero. In math, the absolute value or modulus of a number is its non-negative value or distance from zero.It is symbolized using vertical lines. Here is a look at the absolute value definition, examples, and ways to solve absolute value equations.Apr 8, 2023 · The positive real number 4 is the absolute value of $-4$. In mathematics, the absolute value of a real number is the non-negative value without regard to its sign. For example, the absolute value of $3$ is $3$, and the absolute value of $−3$ is also $3$. The absolute value of a number is denoted by two vertical bars on either side of the ... 1 is the difference between the absolute value of 4 and the absolute value of negative 3.. Here, we have, given that, the difference between the absolute value of 4 and the absolute value of negative 3.. so, we get, Equation= |4| - |-3|=?. now, we know, absolute value of 4 is 4.. i.e. |4| =4A normal absolute eosinophil count ranges from 0 to 500 cells per microliter (<0.5 x 10 9 /L). This typically amounts to less than 5% of all white blood cells. Different laboratories may have different normal reference ranges. Your healthcare provider can explain your results and provide clarity if you have any questions.Absolute Value Equations Quiz. This quiz will put your skills in solving absolute value equations to the test. This quiz contains a total of ten (10) multiple-choice questions. To pass, you'll need a score of 70% or higher. Good luck! Don't miss our new lessons!Apr 2, 2024 · For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line. Furthermore, the absolute value of the difference of two real numbers is the distance between them. The absolute value has the following four fundamental properties: An eosinophil count uses a standard blood draw. As with any blood test, there are minimal risks of experiencing minor bruising at the needle site. In rare cases, the vein may become swollen after ...\[\therefore \]The absolute value of \[4 + 3i\] is 5. Note: Many students make the mistake of writing both the values i.e. \[ + 5\] and \[ - 5\] in the final answer which is wrong as the absolute value or modulus is always positive as it denotes the distance between the complex number and the origin.The absolute maximum and minimum value of f (x)= 3x4 −8x3 +12x2 −48x+25,x ∈ [0,3] are respectively. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:the absolute value of 4xx4 if 0 x 4 is.Explanation: absolute value function like y = |x − 2|. can be written like this: y = √(x −2)2. apply differentiation : y' = 2(x −2) 2√(x − 2)2 → power rule. simplify, y' = x − 2 |x − 2| where x ≠ 2. so in general d dx u = u |u| ⋅ du dx. I will put this on double check just to be sure.Question 448581: what is the absolute value of 4+7i. Answer by jim_thompson5910 (35256) ( Show Source ): You can put this solution on YOUR website! Start with the absolute value of a complex number formula. This is also known as the magnitude of a complex number formula. Plug in and . Square to get.Simply enter two real numbers in the input sections and hit the calculate button to avail the Absolute Difference of two numbers in a matter of seconds. 4. Why is the Absolute Value of a number always positive? Absolute Value is always positive as it is the distance of a number from zero in the number line.In other words it is the magnitude or size of a number, no negatives allowed. The symbol "|" is placed either side to mean "Absolute Value", so we write: |−6| = 6. Try it yourself: Absolute Value. Illustrated definition of Absolute Value: How far a number is from zero. Examples: 6 is 6 away from zero, so the absolute value of 6 is 6 minus6...Ex-1 : We are given an approximate value of π is 22/7 = 3.1428571 and true value is 3.1415926. Calculate absolute, relative and percentage errors? Solution - We have True value X= 3.1415926, And Approx. value X 1 = 3.1428571. So now we calculate Absolute error, we know that E A = X - X 1 =δX Hence E A = 3.1415926- 3.1428571 = -0.0012645 ...Absolute Value I am having an issue with finding the max value of positive and negative values. I want it to always pick the highest integer but to have it's sign remain the same. For instance, x=10, y=15, z=-20 are my numbers calculated that . t:=550*[max(x,y,z)] -p is depended on. if I do r:= max(x,y,z) it will state that r=15 when I need it ...Examples, videos, and solutions to help Grade 6 students understand the absolute value of a number as its distance from zero on the number line. Students use absolute value to find the magnitude of a positive or negative quantity in a real-world situation. New York State Common Core Math Grade 6, Module 3, Lesson 11. Opening Exercises.Also, the absolute value of -4 is written as |-4|. As we discussed earlier, the absolute value results in a non-negative value all the time. Hence, |4|=|-4| =4. That is, it turns negative numbers also into positive numbers. The …Find your Math Personality! What is the absolute value of the complex number -4-√2i? √14, 3√2, 14, 18. Solution: Given complex number is -4 - √2i. The absolute value of a complex number is the distance between the origin and the given point on a complex plane and it can be calculated as follows: |a + ib| = √ (a 2 + b 2) Here, a = -4 ...Answer: Step-by-step explanation: Absolute Value of the number is the distance of the number from zero on the number line. Thus, the absolute value of -8 and 8 is the same i.e. 8. That means, the absolute value of negative or positive of that number is always a positive number of that number.Recall that in its basic form f (x) = |x|, f ( x) = | x |, the absolute value function is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.This page titled 4.4: Absolute Value Inequalities is shared under a CC BY-NC-SA 2.5 license and was authored, remixed, and/or curated by David Arnold via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.Follow the steps mentioned below to find the absolute value of a number using the online absolute value calculator. Step 1: Go to Cuemath's online absolute value calculator. Step 2: Enter any number in the given input box. Step 3: Click on " Calculate " to find the absolute value of the number. Step 4: Click on " Reset " to clear the field and ...Example 4.4.5. Solve for y y: |y + 2| ≤ 5 | y + 2 | ≤ 5. Solution. If we are to use distance to find a solution, our inequality must be converted to the absolute value of a difference. We will use the following property of arithmetic to convert to a difference: A + B = A − (−B) A + B = A − ( − B) Therefore:Absolute Value. In the opening activity, you saw that a difference needs to be calculated in different ways depending on whether the first value is greater or less than the second value. This problem can be solved using absolute value. This concept is often explored by imagining distance above and below zero by comparing it to sea level. The distance of a number from zero (sea level) can be ...Explanation: Absolute value of a negative number is the number opposite to it. So. | −4| = − ( − 4) = 4. Answer link. See explanation.This rule is used for solving most absolute value questions. Absolute value equations Absolute value equations are equations in which the variable is within an absolute value operator. For example: | x-4 | = 10 Because the value of x-4 can be 10 or -10, both of which have an absolute value of 10, we need to consider both cases: x-4 = 10 and x-4 ...the absolute value is never negative; the absolute value of 0 is 0 because the distance between a number and itself is zero. The absolute value of a number a is written as ∣ a ∣ . For example, the absolute value of - 7 is written as | - 7|. Example 1: Find the absolute value of 2. Solution: Graph 2 on a number line. Answer: ∣ 2 ∣ ...The absolute value of a number a, denoted |a|, is the positive distance between the number and zero on the number line. It is the value of the corresponding "unsigned" number -- that is, the number with the sign removed. Boundary Point A value of the variable that makes the equation true when an equal sign is substituted for an inequality sign ...Simply enter two real numbers in the input sections and hit the calculate button to avail the Absolute Difference of two numbers in a matter of seconds. 4. Why is the Absolute Value of a number always positive? Absolute Value is always positive as it is the distance of a number from zero in the number line.Absolute value is a helpful concept when we are only interested in the size of the difference between two numbers. Absolute value gives distance, but discards information about direction. Because direction is ignored, the absolute value of any number can only be positive or zero, never negative. When an expression's value is positive or zero ...1. Set up the equation for the positive value. An equation involving absolute value will have two possible solutions. To set up the positive equation, simply remove the absolute value bars, and solve the equation as normal. [6] For example, the positive equation for is .The absolute value of a number is the number without its sign. Syntax. ABS(number) Number is the real number of which you want the absolute value. Example. Col1. Formula. Description (Result)-4 =ABS([Col1]) Absolute value of -4 (4) Need more help? Want more options? Discover Community.The absolute value of a number a a, denoted |a| | a |, is the distance from a to 0 on the number line. Absolute value answers the question of "how far," and not "which way." The phrase "how far" implies "length" and length is always a nonnegative quantity. Thus, the absolute value of a number is a nonnegative number. Sample Set A.The absolute value of a number is the distance between that number and zero. For instance, the absolute value of 7 is 7, the absolute value of -5 is 5, and the absolute value of 0 is 0 ... If you have a positive value in the absolute value sign, it just is itself. The absolute value of 2 is 2. Then we have the absolute value of 5 minus 15. Well, that's going to be the same thing as the absolute value. 5 minus 15 is negative 10, so it's the same thing as the absolute value of negative 10. Now, there's two ways you can think about it. Solution. Already the absolute value expression is isolated, therefore assume the absolute symbols and solve. | x + 2 | = 7 → x + 2 = 7. Subtract 2 from both sides. x + 2 - 2 = 7 -2. x = 5. Multiply 7 by -1 to solve for the negative version of the equation. x + 2 = -1 (7) → x + 2 = -7. Subtract by 2 on both sides.Jun 17, 2021 · The absolute value of a number a a, denoted |a| | a |, is the distance from a to 0 on the number line. Absolute value answers the question of "how far," and not "which way." The phrase "how far" implies "length" and length is always a nonnegative quantity. Thus, the absolute value of a number is a nonnegative number. Sample Set A. Absolute value of a number is the distance between the number and a zero on a number line. And distance is always positive. so absolute value of any number a is | a | | a| = a if a > 0 = 0 if a = 0 = - a if a < 0. as 4/5 > 0. Hence absolute value of 4/5 is 4/5 itself. absolute value of 4/5 is 4/5. Learn More: sum of rational numbers whose ...The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval. This makes sense: when a function is continuous you can draw its graph without lifting the pencil, so you must hit a high point and a low point on that interval. Created by Sal Khan.This page titled 4.4: Absolute Value Inequalities is shared under a CC BY-NC-SA 2.5 license and was authored, remixed, and/or curated by David Arnold via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.Mathematically, we take the absolute value of the result. We will ignore this detail from now on, while remembering to interpret elasticities as positive numbers. This means that, along the demand curve between point (B) and (A), if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a ...You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: The absolute value of the sum of 4 times a number and 7 is the sum of 2 times a number and 3. Write and solve an absolute value equation to represent the situation. The absolute value of the sum of 4 times a number and 7 is the sum of 2 ...And just as a reminder, absolute value literally means-- whether we're talking about a complex number or a real number, it literally just means distance away from 0. So the absolute value of 3 minus 4i is going to be the distance between 0, between the origin on the complex plane, and that point, and the point 3 minus 4i. The absolute value of 9 is 9. (9 is 9 places from 0.) The absolute value of -4 is 4. (-4 is 4 places from 0.) The absolute value of 0 is 0. (0 is 0 places from 0.) We work with the understanding that 9 and 4 don't tell which side of zero 9 and -4 are on. The absolute value simply tells how far these numbers are from 0. Correct answer: f (x) = x 4 + (1 – x) 2. Explanation: When we take the absolute value of a function, any negative values get changed into positive values. Essentially, | f ( x )| will take all of the negative values of f ( x) and reflect them across the x -axis. However, any values of f ( x) that are positive or equal to zero will not be ...The absolute value function is commonly used to measure distances between points. Applied problems, such as ranges of possible values, can also be solved using the absolute value function. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.We could say that the absolute value of a number is its purely arithmetical value. Here is the algebraic definition of | x |: If x ≥ 0, then | x | = x; if x < 0, then | x | = − x. That is, if x is non-negative: |3|, then the absolute value is the number itself. If x is negative: |−3|, then the absolute value is its negative; that makes ...|4-8i|=sqrt{4^2+(-8)^2}=sqrt(16+64)=sqrt80=4sqrt5. Taking, sqrt5~=2.236, |z|~=4xx2.236=8.944 Absolute Value or Modulus |z|of a Complex No. z=x+iy is defined by, |z ...One way of thinking of the concept of absolute numbers is that it is the distance of that number from 0 – -4 is four away from 0, while 4 is also four away from 0. Example. What is the absolute value of the following numbers? -4, -18.2, and 17 1/3-4 – the absolute value is 4, as -4 is four numbers from 0.-18.2 – the absolute value is 18.2 ...Join with Mr. B as we understand opposite numbers and absolute values. In this mathematics tutorial you'll find a visual mini-lesson along with practice and ...Remove the absolute value brackets and solve the equation for 2 different cases. STEP 3: Check to see whether each solution is valid by putting each one back into the original equation and verifying that the two sides of the equation are equal. - In CASE 1, the solution, w = 22, is valid because 12 + | 22 - 4 | = 12 + 18 = 30.Includes lessons Absolute Value Solution Sets, Absolute Value Inequalities with One Variable, and Absolute Value Inequalitiea with Two Variables.Test prep. Improve your math knowledge with free questions in "Absolute value of rational numbers" and thousands of other math skills.After determining that the absolute value is equal to 4 at x = 1 x = 1 and x = 9, x = 9, we know the graph can change only from being less than 4 to greater than 4 at these values. This divides the number line up into three intervals: x < 1, 1 …
Take out all the face cards and jokers and divide the deck between two people. 1) Each player lays down one card at a time. 2) Find the absolute value of each card. The player with the highest absolute value wins that round and takes both cards. 3) Continue until all cards have been played. . What lang
Therefore its absolute value is 9. The number -9 is the same distance from zero, so its absolute value is also just 9. In both cases the magnitude, or absolute value, of your number is just plain old "9" because you've removed any negative sign that might have existed. Taking absolute value of a number leaves a positive unchanged, and makes a ... Therefore, the answer to "What two numbers have an absolute value of 4?" is: 4 and -4. The absolute value of 4 is 4 and the absolute value of -4 is also 4. Here it is expressed mathematically with vertical lines that we call bars: For future reference, remember that the two numbers that have an absolute value of x are x and -x. The absolute value of the sum of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4 x + 3 y − 10 = 0 is_____ View Solution If the equations x 2 − 3 x + 4 = 0 and x ( b − 3 x ) + 2 x + a = 0 have a common root then the absolute value of ( a − b ) is equal toJust put in the numbers and let PowerShell do the math! Four operations with PowerShell. If you wish, you can also use variables, which is much easier when it comes to multiple complex operations. PowerShell …Best Answer. Copy. The absolute value of a number is the distance from that number to 0. Therefore, the absolute value is ALWAYS positive. the absolute value of -4.2 is 4.2. To find the absolute value, just determine how far it is from 0. Wiki User.Therefore, the answer to "What two numbers have an absolute value of 4?" is: 4 and -4. The absolute value of 4 is 4 and the absolute value of -4 is also 4. Here it is expressed mathematically with vertical lines that we call bars: For future reference, remember that the two numbers that have an absolute value of x are x and -x.The absolute value of any number is either zero [latex](0)[/latex] or positive. It makes sense that it must always be greater than any negative number. The answer to this case is always all real numbers. Examples of How to Solve Absolute Value Inequalities. Example 1: Solve the absolute value inequality.The absolute value of -4 is 4, because it is four units to the right of zero on the number line. Learn how to simplify, compare and use absolute values with examples and exercises.Lesson. The absolute value of a number is its distance from zero (0) on a number line. This action ignores the "+" or "-" sign of a number because distance in mathematics is never negative. You identify an absolute value of a number by writing the number between two vertical bars referred to as absolute value brackets: |number|.3. I would guess it is your first option. A usual terminology in calculus is about absolute and relative (or local) maxima and minima. The absolute maximum would be then max{f(x): x ∈ [−2, 4]} max { f ( x): x ∈ [ − 2, 4] }. The phrase "absolute maximum value " probably has to do with the fact that when looking at extrema of functions ...Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Absolute Value and Evaluat...http://www.greenemath.com/In this video we explain how to find the absolute value of a number. What is the absolute value of a number? The absolute value of ...Click here 👆 to get an answer to your question ️ The absolute value of 4+7i is equal to the square root of Gauthmath has upgraded to Gauth now! 🚀 Calculator Download Gauth PLUSShift absolute value graphs Get 3 of 4 questions to level up! Scale & reflect absolute value graphs Get 3 of 4 questions to level up! Graph absolute value functions Get 3 of 4 questions to level up! Quiz 1. Level up on the above skills and collect up to 240 Mastery points Start quiz. Piecewise functions.pandas.Series.abs. #. Return a Series/DataFrame with absolute numeric value of each element. This function only applies to elements that are all numeric. Series/DataFrame containing the absolute value of each element. Calculate the absolute value element-wise. For complex inputs, 1.2 + 1j, the absolute value is a 2 + b 2..