Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 714: 68


$-i\pm i\sqrt{1-i}$

Work Step by Step

$i{{x}^{2}}-2x+1=0$ Now compare the equation $i{{x}^{2}}-2x+1=0$ with the standard form of the quadratic equation $a{{x}^{2}}+bx+c=0$. Here, $a=i,b=-2$and $c=1$ Substitute $a=i,b=-2$ and $c=1$ into the quadratic formula $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$. $\begin{align} & x=\frac{-\left( -2 \right)\pm \sqrt{{{\left( -2 \right)}^{2}}-4\left( i \right)\left( 1 \right)}}{2\left( i \right)} \\ & =\frac{2\pm \sqrt{4-4i}}{2i} \\ & =\frac{2\pm 2\sqrt{1-i}}{2i} \\ & =\frac{1\pm \sqrt{1-i}}{i} \end{align}$ Rationalize the expression by multiplying by $\frac{i}{i}$, $\begin{align} & x=\frac{1\pm \sqrt{1-i}}{i}\cdot \frac{i}{i} \\ & =\frac{i\pm i\sqrt{1-i}}{{{i}^{2}}} \\ & =\frac{i\pm i\sqrt{1-i}}{-1} \\ & =-i\pm i\sqrt{1-i} \end{align}$
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