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Polygon in Complex Plane

Source: AMC 12 2008A #23

February 17, 2008
geometrysymmetrygeometric transformationrotationanalytic geometrytrigonometryAoPSwiki

Problem Statement

The solutions of the equation z^4 \plus{} 4z^3i \minus{} 6z^2 \minus{} 4zi \minus{} i \equal{} 0 are the vertices of a convex polygon in the complex plane. What is the area of the polygon? <spanclass=′latex−bold′>(A)</span> 25/8<spanclass=′latex−bold′>(B)</span> 23/4<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 25/4<spanclass=′latex−bold′>(E)</span> 23/2 <span class='latex-bold'>(A)</span>\ 2^{5/8} \qquad <span class='latex-bold'>(B)</span>\ 2^{3/4} \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ 2^{5/4} \qquad <span class='latex-bold'>(E)</span>\ 2^{3/2}
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