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: 1

Answer

{$-8i,8i$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x)^{2}=-64$ Step 2: $x=\pm \sqrt {-64}$ Step 3: $x=\pm \sqrt {-1\times64}$ Step 4: $x=\pm \sqrt {-1}\times\sqrt {64}$ Step 5: $x=\pm (i\times\sqrt {64})$ [as $i=\sqrt {-1}$] Step 6: $x=\pm (i\times8)$ Step 7: $x=\pm (8i)$ Step 8: $x=8i$ or $x=-8i$ Therefore, the solution set is {$-8i,8i$}.
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