# An algebra problem by Rakshit Joshi

Algebra Level 3

$\left(z+\frac{1}{z}\right)^2 + \left(z^2+ \frac{1}{z^2}\right)^2 +\left(z^3 + \frac{1}{z^3}\right)^2 +\cdots + \left(z^{24}+\frac{1}{z^{24}}\right)^2$

If $$z^2-z+1=0$$, then find the value of the expression above.

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