The value of $(1 + i)^{5} \times (1 - i)^{5}$

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Solution

Given that,
$(1 + i)^{5} (1 - i)^{5}$
$= [(1 + i) (1 - i)]^{5}$
$= [(1^{2} - i^{2})]^{5}$
$= [1 - (- 1)]^{5}$ $[∵ i^{2} = - 1]$
$= [1 + 1]^{5}$
$= 32$

Hence, this is the required solution.

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