Answer
$x^4-2x^3+3x^2-2x+2$
Work Step by Step
Step 1. Given zeros $x=i, 1+i$, we can identify another two zeros $x=-i, 1-i$
Step 2. We can write the function as $f(x)=(x-i)(x+i)(x-1-i)(x-1+i)=(x^2+1)(x^2-2x+2)=x^4-2x^3+3x^2-2x+2$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 4 - Polynomial and Rational Functions - Chapter Review - Review Exercises - Page 244: 44
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