SOLUTION: How do I find the Absolute Value of a complex number? Thank You.

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Question 175558This question is from textbook
: How do I find the Absolute Value of a complex number?
Thank You. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
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The absolute value of any complex number in the form a%2Bbi is abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29. Remember, absolute value geometrically is the distance from the origin. So in this case, we're finding the distance is from the point (a,b) to the origin (0,0) (in the complex plane)


Example:


Problem:
Find the absolute value of 3-6i.


Solution:

In this case, a=3 and b=-6


abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29 Start with the given formula.


abs%283-6i%29=sqrt%28%283%29%5E2%2B%28-6%29%5E2%29 Plug in a=3 and b=-6


abs%283-6i%29=sqrt%289%2B36%29 Square 3 to get 9. Square -6 to get 36


abs%283-6i%29=sqrt%2845%29 Add


abs%283-6i%29=3%2Asqrt%285%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)



So the absolute value of 3-6i is 3%2Asqrt%285%29 which approximates to 6.708