Complex solutions of a quintic equation – math.stackexchange.com

Solve $$z^5+4\overline z^3=0$$ This is what I did. Let $z=r(\cos\theta+i\sin\theta)$ so, the equation is: $$r^5(\cos5\theta+i\sin5\theta)+4r^3(\cos3\theta-i\sin3\theta)=0.$$ Suppose $r$ is not $0$ ...

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