MathDB
Complex Equation

Source:

January 21, 2006
algebrapolynomial

Problem Statement

Suppose z=a+biz=a+bi is a solution of the polynomial equation c4z4+ic3z3+c2z2+ic1z+c0=0c_4z^4+ic_3z^3+c_2z^2+ic_1z+c_0=0, where c0c_0, c1c_1, c2c_2, c3c_3, aa, and bb are real constants and i2=−1i^2=-1. Which of the following must also be a solution?
<spanclass=′latex−bold′>(A)</span>−a−bi<spanclass=′latex−bold′>(B)</span>a−bi<spanclass=′latex−bold′>(C)</span>−a+bi<spanclass=′latex−bold′>(D)</span>b+ai<spanclass=′latex−bold′>(E)</span>none of these<span class='latex-bold'>(A) </span> -a-bi\qquad <span class='latex-bold'>(B) </span> a-bi\qquad <span class='latex-bold'>(C) </span> -a+bi\qquad <span class='latex-bold'>(D) </span>b+ai \qquad <span class='latex-bold'>(E) </span> \text{none of these}
Back to ProblemsView on AoPS