Hi guys, need help with this question:

Show that the roots of the EQN z^5 - (z - i)^5 = 0, z is not equal to i, are

(1/2)[cot(k(pi)/5) + i] where k = 1,2,3,4.

Thanks in advance!

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- Jun 2nd 2011, 07:54 PMBlizzardyComplex Numbers: Roots of an EQN
Hi guys, need help with this question:

Show that the roots of the EQN z^5 - (z - i)^5 = 0, z is not equal to i, are

(1/2)[cot(k(pi)/5) + i] where k = 1,2,3,4.

Thanks in advance! - Jun 2nd 2011, 08:42 PMTKHunny
Since z = i is not a solution, I'm puzzled by the question.

- Jun 2nd 2011, 09:55 PMProve It
- Jun 3rd 2011, 03:06 AMAckbeet
Try this line of reasoning:

Let

Then the fifth roots of unity (exactly). So I would try writing down the 's, and then solving for once you've done that.

Make sense?