Find the value of $(1 + i)^{8}$

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Solution

We have,
Let, $x = [(1 + i)^{2}]$
$(1 + i)^{4} = [(1 + i)^{2}] \times [(1 + i)^{2}]$
$= (1 + i)^{4} = x^{2}$
Let solve for $(x)$
$x = (1 + i)^{2}$
$= 1 + i^{2} + 2 i$
$= 1 + (- 1) + 2 i$
$= 2 i$
So, basically
$(1 + i)^{4} = (2 i) \times (2 i)$
$= 4 (i)^{2}$
$= - 4$
Hence, this is answer.

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