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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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?
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