SOLUTION: complex number in polar form (5+5i)^3

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Question 1178087: complex number in polar form
(5+5i)^3
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
First put it into exponential form: re%5E%28i%2Atheta%29+
where r = sqrt%28a%5E2%2Bb%5E2%29 = 5%2Asqrt%282%29
and theta = tan%5E-1%28b%2Fa%29 = tan%5E-1%281%29+ = 45%5Eo


Now +%285%2B5i%29%5E3+ = +%285%2Asqrt%282%29%29%5E3+%2A+e%5E%28%283%2A45%29%2Ai%29+
You can finish the calculation.
Once you have the answer in exponential form, you can write it in polar form (trivially) using this:
+r%2Ae%5E%28i%2Atheta%29+=+r%2Acos%28theta%29%2Bi%2Ar%2Asin%28theta%29+