Question

Evaluate:$i^{-9999}$

Answer 1

$i^{-9999}$

$=\frac{1}{i^{9999}}$

$=\frac{1}{i^{2000-1}}$

$=\frac{1}{i^{2000}{i}^{-1}}$

$=\frac{i}{i^{2000}}$ since $\frac{1}{a^m}=a^{-m}$

$=\frac{i}{{\left(i^4\right)}^{500}}$

We know that $i^2=-1\Rightarrow i^4={(-1)}^2=1$

$=\frac{i}{1^{500}}$

$=i$