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Contrived Equation in Complex Numbers

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April 6, 2013
quadraticscomplex numbersalgebraquadratic formulapolynomialRational Root Theorem

Problem Statement

The equation z(z+i)(z+3i)=2002iz(z+i)(z+3i)=2002i has a zero of the form a+bia+bi, where aa and bb are positive real numbers. Find aa.
<spanclass=′latex−bold′>(A)</span>118<spanclass=′latex−bold′>(B)</span>210<spanclass=′latex−bold′>(C)</span>2210<spanclass=′latex−bold′>(D)</span>2002<spanclass=′latex−bold′>(E)</span>1002<span class='latex-bold'>(A) </span>\sqrt{118}\qquad<span class='latex-bold'>(B) </span>\sqrt{210}\qquad<span class='latex-bold'>(C) </span>2\sqrt{210}\qquad<span class='latex-bold'>(D) </span>\sqrt{2002}\qquad<span class='latex-bold'>(E) </span>100\sqrt2
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