Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 240: 9

Answer

$-i$ and $1-i$

Work Step by Step

The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. Its degree is $4$, hence it has $4$ complex (including real) zeros. $2$ zeros are already given, hence there are only $2$ zeros left which are $-i$ and $1-i$ (the conjugates of $i$ and $1+i$, respectively) according to the Conjugate Pairs Theorem.
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