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: 30

Answer

$\displaystyle-\frac{1}{2}+\frac{5}{2}i$

Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain: $\displaystyle \frac{2+3i}{1-i}$ $\displaystyle=\frac{2+3i}{1-i}*\frac{1+i}{1+i}$ $\displaystyle=\frac{2+2i+3i+3i^{2}}{1+i-i-i^{2}}$ $\displaystyle=\frac{2+5i+3*-1}{1--1}$ $\displaystyle=\frac{-1+5i}{2}$ $\displaystyle=-\frac{1}{2}+\frac{5}{2}i$
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