Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 3

Answer

{$2-i,2+i$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x-2)^{2}=-1$ Step 2: $x-2=\pm \sqrt {-1}$ Step 3: $x=2\pm \sqrt {-1}$ Step 4: $x=2\pm i$ [as $i=\sqrt {-1}$] Step 5: $x=2+i$ or $x=2-i$ Therefore, the solution set is {$2-i,2+i$}.
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