# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 60

$-3-4i$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $(1-2i)^2 ,$ simplifies to \begin{array}{l}\require{cancel} (1)^2+2(1)(-2i)+(-2i)^2 \\\\= 1-4i+4i^2 \\\\= 1-4i+4(-1) \\\\= 1-4i-4 \\\\= -3-4i .\end{array}

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