SOLUTION: Absolute value of -1+3i

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Question 423401: Absolute value of -1+3i
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In general the absolute value of something is it distance from zero. In the case of a complex number, a+bi, its absolute value is its distance from the zero complex number, 0+0i.

If you have learned how to plot complex numbers on a coordinate system you can plot the two points and see that the distance between a+bi and 0+0i can be found with the distance formula, d+=+sqrt%28%28x%5B2%5D+-+x%5B1%5D%29%5E2+%2B+%28y%5B2%5D+-+y%5B1%5D%29%5E2%29. So
abs%28a%2Bbi%29+=+sqrt%28%28a-0%29%5E2+%2B+%28b-0%29%5E2%29
which simplifies to:
abs%28a%2Bbi%29+=+sqrt%28a%5E2+%2B+b%5E2%29
Some people just memorize this formula. Others figure it out from the distance formula.

Now that we have a formula for absolute value of a complex number we can use it on your complex number:
abs%28-1%2B3i%29+=+sqrt%28%28-1%29%5E2+%2B+%283%29%5E2%29
which simplifies as follows:
abs%28-1%2B3i%29+=+sqrt%281+%2B+9%29
abs%28-1%2B3i%29+=+sqrt%2810%29
Since sqrt%2810%29 does not simplify further we are finished.