College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 73

Answer

$x=\pm 2i$ or $x=\pm 3i$

Work Step by Step

We solve by factoring: $x^{4}+13x^{2}+36=0$ $(x^{2}+4)(x^{2}+9)=0$ $x^{2}+4=0$ or $x^{2}+9=0$ $x^{2}=-4$ or $x^{2}=-9$ $x=\pm\sqrt{-4}$ or $x=\pm\sqrt{-9}$ $x=\pm 2i$ or $x=\pm 3i$ Recall, $i=\sqrt{-1}$
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