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}
