Question:
Evaluate $\frac{1}{\mathrm{i}^{78}}$
Solution:
we have $\frac{1}{\mathrm{i}^{78}}$
$=\frac{1}{\left(i^{4}\right)^{19} \cdot i^{2}}$
We know that, $i^{4}=1$
$\Rightarrow \frac{1}{1^{19} \cdot \mathrm{i}^{2}}$
$\Rightarrow \frac{1}{\mathrm{i}^{2}}=\frac{1}{-1}$
$\Rightarrow \frac{1}{\mathrm{i}^{78}}=-1$