Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises - Page A56: 21


$-1\pm 2i$

Work Step by Step

$x^{2}+2x+5=0$ We solve using the quadratic formula (a=1, b=2, c=5): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\displaystyle \frac{-2\pm\sqrt{2^{2}-4(1)(5)}}{2(1)}$ $=\frac{-2\pm\sqrt{-16}}{2}$ $=\frac{-2\pm\sqrt{-1*16}}{2}$ We use the fact that $\sqrt{-1}=i$: $=\frac{-2\pm 4i}{2}$ $=-1\pm 2i$
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