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

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Solution

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

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