SOLUTION: 7. Find the cube roots of 1-i

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Question 1080584: 7. Find the cube roots of 1-i
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
r=sqrt%281%5E2%2B%28-1%29%5E2%29=sqrt%281%2B1%29=sqrt%282%29
and
theta=tan%5E%28-1%29%28-1%2F1%29=%287%2F4%29pi
So then for the cube root, the modulus would be
root%283%2Csqrt%282%29%29=root%286%2C2%29
For the angle,
A%5B1%5D=%281%2F3%29%287%2F4%29pi=%287%2F12%29pi
A%5B2%5D=%281%2F3%29%287%2F4%29pi%2B1%2A%282pi%29%2F3=%285%2F4%29pi
A%5B3%5D=%281%2F3%29%287%2F4%29pi%2B2%2A%282pi%29%2F3=%2823%2F12%29pi
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z%5B1%5D=root%286%2C2%29%2A%28cos%28%287%2F12%29pi%29%2Bi%2Asin%28%287%2F12%29pi%29%29
z%5B2%5D=root%286%2C2%29%2A%28cos%28%285%2F4%29pi%29%2Bi%2Asin%28%285%2F4%29pi%29%29
z%5B3%5D=root%286%2C2%29%2A%28cos%28%2823%2F12%29pi%29%2Bi%2Asin%28%2823%2F12%29pi%29%29