Question

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

Answer 1

$(1-i{)}^4=[(1-i{)}^2{]}^2$

$=[1^2+i^2-2i{]}^2$

$=[1-1-2i{]}^2$

$=(-2i{)}^2$

$=(-2i)\times (-2i)$

$=4i^2$

$=-4+\left(0\right)i$, which is in the form $a+ib$