College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 68


$\displaystyle \frac{1}{2}\pm\frac{\sqrt{3}}{2}i$

Work Step by Step

Use the quadratic formula $a=1, b=-1, c=1$ $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ $x=\displaystyle \frac{1\pm\sqrt{1-4}}{2}=\frac{1\pm\sqrt{-3}}{2}$ ...If $N$ is a positive real number, we define the principal square root of $-N,$ denoted by $\sqrt{-N},$ as $\sqrt{-N}=\sqrt{N}i$ $=\displaystyle \frac{1\pm i\sqrt{3}}{2}$ $=\displaystyle \frac{1}{2}\pm\frac{\sqrt{3}}{2}i$
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