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Complex Dodecagon

Source: 2017 AMC 12B #12

February 16, 2017
AMCAMC 12AMC 12 B2017 AMC 12Bcomplex numbers

Problem Statement

What is the sum of the roots of z12=64z^{12} = 64 that have a positive real part?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>2+23<spanclass=′latex−bold′>(D)</span>22+6<spanclass=′latex−bold′>(E)</span>(1+3)+(1+3)i<span class='latex-bold'>(A) </span>2 \qquad<span class='latex-bold'>(B) </span>4 \qquad<span class='latex-bold'>(C) </span>\sqrt{2} +2\sqrt{3}\qquad<span class='latex-bold'>(D) </span>2\sqrt{2}+ \sqrt{6} \qquad<span class='latex-bold'>(E) </span>(1 + \sqrt{3}) + (1+\sqrt{3})i
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