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: 43

Answer

$-2+2i$

Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we use the distributive property to obtain: $(1+i)^{3}$ $=(1+i)(1+i)(1+i)$ $=(1+2i+i^{2})(1+i)$ $=(1+2i+-1)(1+i)$ $=(2i)(1+i)$ $=2i+2i^{2}$ $=2i+2*-1$ $=-2+2i$
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