Thread: Complex 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!

Since z = i is not a solution, I'm puzzled by the question.

Originally Posted by Blizzardy

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!

Why not start by expanding and simplifying before trying to solve the equation?

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?