Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 64

Answer

$x=-1\pm i$

Work Step by Step

$x^{2}+2x+2=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=2$ and $c=2$. Substitute the known values in the formula: $x=\dfrac{-2\pm\sqrt{2^{2}-4(1)(2)}}{2(1)}=\dfrac{-2\pm\sqrt{4-8}}{2}=...$ $...=\dfrac{-2\pm\sqrt{-4}}{2}=\dfrac{-2\pm2i}{2}=-1\pm i$ The solution is $x=-1\pm i$
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