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: 2

Answer

{$-7i,7i$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x)^{2}=-49$ Step 2: $x=\pm \sqrt {-49}$ Step 3: $x=\pm \sqrt {-1\times49}$ Step 4: $x=\pm \sqrt {-1}\times\sqrt {49}$ Step 5: $x=\pm (i\times\sqrt {49})$ [as $i=\sqrt {-1}$] Step 6: $x=\pm (i\times7)$ Step 7: $x=\pm (7i)$ Step 8: $x=7i$ or $x=-7i$ Therefore, the solution set is {$-7i,7i$}.
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