# An algebra problem by Keshav Tiwari

Algebra Level 5

Let $$z = x + iy$$ for real numbers $$x$$ and $$y$$, and $$x \ne -\dfrac12$$.

Find the number of values of $$z$$ satisfying $$|z|^{n} = z^{2} |z|^{n-2} +z|z|^{n-2} +1$$ for natural number $$n> 1$$.

 Clarification: $$i=\sqrt{-1}$$.

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