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2021 MECC Mock AMC 12

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Problem 21

The exact value of $\sqrt{\sqrt{\sqrt{\sqrt{\frac{-1-\sqrt{3}i}{2}}}}}$ can be expressed as $\frac{\sqrt{a}+\sqrt{b}+i\sqrt{c}-i\sqrt{d}}{e}$ which the fraction is in the most simplified form and $a$, $b$, $c$, $d$ and $e$ are not necessary distinct positive integers. Find $2a+b+2c+d+e$

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