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## Homework Statement

Solve z^5 + 16 conjugate(z) = 0 for z element of C.

z^5 + 16z' = 0

http://puu.sh/2EBqC.png [Broken]

## Homework Equations

## The Attempt at a Solution

My first thought was to use z = a+bi and z' = a-bi

So:

(a+bi)5 + 16*(a-bi) = 0 + 0i And then expand and simplify to the real and non real parts. http://puu.sh/2EBwU.png [Broken]

But it seems WAAY too complicated for a question worth only 4 marks.

I would appreciate if someone could post their thoughts.

Thanks!

According to WolframAlpha: http://puu.sh/2EBKH.png [Broken]

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