Question:
Express the given complex number in the form $a+i b:(1-i)^{4}$
Solution:
$(1-i)^{4}=\left[(1-i)^{2}\right]^{2}$
$=\left[1^{2}+i^{2}-2 i\right]^{2}$
$=[1-1-2 i]^{2}$
$=(-2 i)^{2}$
$=(-2 i) \times(-2 i)$
$=4 i^{2}=-4 \quad\left[i^{2}=-1\right]$
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