(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give under the exponential form all non-zero solutions of (z^{3}) + (4conjugate(z^{2})) = 0

2. Relevant equations

z=x+iy where i^{2}=-1

z^{n}=r^{n}(cos(nθ)+isin(nθ))

3. The attempt at a solution

First i tried expanding by making z=x+iy so x^{3}+3ix^{2}y+4x^{2}-3xy^{2}-8ixy-iy^{3}-4y^{2}=0, but then I have no idea on how to get the solutions out of this mess.

Then I tried putting it into exponential and using roots:

z^{3}=-4conjugate(z^{2})

z=(-4)^{1/3}r^{2/3}(cos((2θ+2πk)/3)-sin((2θ+2πk)/3))

And now I have no idea what to do... :S

Thank you for your time

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# Homework Help: Find solutions of complex equation

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