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I think I spoiled this one

Source: 2017 AMC 12A #17

February 8, 2017
2017 AMC 12AAMC 12AMCcomplex numbers

Problem Statement

There are 24 different complex numbers zz such that z24=1z^{24} = 1. For how many of these is z6z^6 a real number?
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>6<spanclass=latexbold>(D)</span>12<spanclass=latexbold>(E)</span>24<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>12\qquad<span class='latex-bold'>(E) </span>24