Question

Find the value of ${(-\sqrt{-1})}^{4n+3}$, when $n$ is a positive integer.

Answer 1

$(-\sqrt{-1}{)}^{4n+3}$

$=(-\text{i}{)}^{4n+3}$

$=-(\text{i}{)}^{4n+3}$

$=-(-\text{i})$

$=\text{i}=\sqrt{-1}$