z^7 - i = 0

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

Thank you in advance

Printable View

- Aug 19th 2009, 01:25 AMpadixiongFind all the complex solutions
z^7 - i = 0

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

Thank you in advance - Aug 19th 2009, 02:01 AMred_dog
$\displaystyle z^7=i\Rightarrow z^7=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}$

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