1982 AHSME Problems/Problem 27

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Problem

Suppose $z=a+bi$ is a solution of the polynomial equation \[c_4z^4+ic_3z^3+c_2z^2+ic_1z+c_0=0,\] where $c_0, c_1, c_2, c_3, a,$ and $b$ are real constants and $i^2=-1.$ Which of the following must also be a solution?

$\textbf{(A)}\ -a-bi\qquad  \textbf{(B)}\ a-bi\qquad  \textbf{(C)}\ -a+bi\qquad  \textbf{(D)}\ b+ai \qquad  \textbf{(E)}\ \text{none of these}$

Solution

See Also

1982 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 26
Followed by
Problem 28
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