2019 AMC 12A Problems/Problem 21

Problem

Let $z=\frac{1+i}{\sqrt{2}}.$ What is $(z^{1^2}+z^{2^2}+z^{3^2}+\dots+z^{{12}^2}) \cdot (\frac{1}{z^{1^2}}+\frac{1}{z^{2^2}}+\frac{1}{z^{3^2}}+\dots+\frac{1}{z^{{12}^2}})?$ $\textbf{(A) } 18 \qquad \textbf{(B) } 72-36\sqrt2 \qquad \textbf{(C) } 36 \qquad \textbf{(D) } 72 \qquad \textbf{(E) } 72+36\sqrt2$

Solution

2019 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
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All AMC 12 Problems and Solutions

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2019 AMC 12A Problems/Problem 21

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