Browse Questions

The value of $\;(-\sqrt{-1})^{4n-3}\;$ , where $\;n \in N \;$ is

$(a)\;-2i\qquad(b)\;-1\qquad(c)\;-i\qquad(d)\;4$

Answer : $\;-i$
Explanation :
$\;(-\sqrt{-1})^{4n-3}\; = (-i)^{4n-3} = (-i)^{4n} \; . (-i)^{-3}$
$= \large\frac{1}{(-i)^{3}} = \large\frac{1}{i}$
$= \large\frac{i}{i^{2}} = -i$