# That's a complex equation!

Geometry Level pending

$(E): ({ z }^{ 2 }-2z)\cos ^{ 2 }{ \alpha +1=0 }$

The equation $$(E)$$ admits 2 solutions $$U$$ and $$V$$. If $$U\times V=\cos ^{ n } \alpha$$, find $$n$$.

Bonus: Find the set of images of these solutions.

Clarification: $$z$$ is a complex number.

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