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: 63


$\displaystyle \frac{1}{4}\pm\frac{1}{4}i$

Work Step by Step

$8x^{2}-4x+1=0$ We solve using the quadratic formula ($a=8,\ b=-4,\ c=1$): $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4(8)(1)}}{2(8)}$ $\displaystyle x=\frac{-(-4)\pm\sqrt{16-32}}{2(8)}$ $\displaystyle x=\frac{+4\pm\sqrt{-16}}{16}$ $\displaystyle x=\frac{4\pm 4i}{16}=\frac{1}{4}\pm\frac{1}{4}i$ Recall, $i=\sqrt{-1}$
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