College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.4: 36

Answer

$(-2+\sqrt{-11})^{2}=-7-4\sqrt{11}i$

Work Step by Step

$(-2+\sqrt{-11})^{2}$ Evaluate the power: $(-2+\sqrt{-11})^{2}=(-2)^{2}+(2)(-2)(\sqrt{-11})+(\sqrt{-11})^{2}=...$ $...=4-4\sqrt{-11}-11=-7-4\sqrt{-11}=...$ Rewrite $\sqrt{-11}$ as $(\sqrt{-1})(\sqrt{11})$: $...=-7-4(\sqrt{-1})(\sqrt{11})=...$ Substitute $\sqrt{-1}$ by $i$ and simplify: $...=-7-4\sqrt{11}i$
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