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: 4

Answer

{$-3-4i,-3+4i$}

Work Step by Step

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