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: 34

Answer

$-2i$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ (1-i)^2 ,$ use the square of a binomial and the equivalence $i^2=-1.$ $\bf{\text{Solution Details:}}$ Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (1)^2-2(1)(i)+(i)^2 \\\\= 1-2i+i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 1-2i+(-1) \\\\= 1-2i-1 \\\\= -2i .\end{array}
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