Elementary Algebra

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

Chapter 11 - Additional Topics - Chapter 11 Test: 11

Answer

{$2-4i,2+4i$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x-2)^{2}=-16$ Step 2: $x-2=\pm \sqrt {-16}$ Step 3: $x-2=\pm \sqrt {-1\times16}$ Step 4: $x-2=\pm (\sqrt {-1}\times\sqrt {16})$ Step 5: $x-2=\pm (i\times4)$ [as $i=\sqrt{-1}$] Step 6: $x-2=\pm 4i$ Step 7: $x-2=4i$ or $x-2=-4i$ Step 8: $x=2+4i$ or $x=2-4i$ The solution set is {$2-4i,2+4i$}.
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