Question

Express the given complex number in the form $a+ib:$${(1-i)}^4$

Answer 1

${(1-i)}^4={\left[{(1-i)}^2\right]}^2$
$={[1^2+i^2-2i]}^2$
$={[1-1-2i]}^2$
$={(-2i)}^2$
$=(-2i)\times (-2i)$
$=4i^2=-4,[\because i^2=-1]$
$=a+ib$, where $a=-4,$ and $b=0$