# Find all the complex solutions

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• August 19th 2009, 01:25 AM
padixiong
Find all the complex solutions
z^7 - i = 0

the answer need to be in polar form between - pie to pie.

Thank you in advance
• August 19th 2009, 02:01 AM
red_dog
$z^7=i\Rightarrow z^7=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}$

Then, $z_k=\cos\frac{\frac{\pi}{2}+2k\pi}{7}+i\sin\frac{\ frac{\pi}{2}+2k\pi}{7}, \ k=0,1,\ldots ,6$