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  4. The value of (1+i)4(1+(1/i))4 is

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Q. The value of $(1+i)^{4}\left(1+\frac{1}{i}\right)^{4}$ is

Complex Numbers and Quadratic Equations

Solution:

$(1+i)^{4} \times\left(1+\frac{1}{i}\right)^{4}=(1+i)^{4} \times(1-i)^{4}$
$=\left(1-i^{2}\right)^{4}=(1+1)^{4}=2^{4}=16$