Express the given complex number in the form a + ib: (1 – i)4
Question:

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

Solution:

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

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

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

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

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

$=4 i^{2}=-4 \quad\left[i^{2}=-1\right]$