Appendix A - Review - A.7 Complex Numbers; Quadratic Equations in the Complex Number System - A.7 Assess Your Understanding - Page A60: 34

$-2i$

Use special formula $(a-b)^2=a^2-2ab+b^2$. We have $a= 1$ and $b=i $ $(1-i)^2=(1)^2-2(1)(i)+(i)^2$ Simplify. $=1-2i+i^2$ Use $i^2=-1$. $=1-2i-1$ Simplify. $=-2i$ Hence, the solution in the standard form is $-2i$.