Question

compute ( i^{-1} ).

Explanation:

Step1: Rewrite negative exponent

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

Step2: Rationalize the denominator

Multiply numerator and denominator by $i$:
$\frac{1}{i} \times \frac{i}{i} = \frac{i}{i^2}$

Step3: Substitute $i^2=-1$

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

Answer:

$-i$