Question

compute ( i^{-5} ).

Explanation:

Step1: Rewrite negative exponent

$i^{-5} = \frac{1}{i^5}$

Step2: Simplify $i^5$ using $i^4=1$

$i^5 = i^4 \cdot i = 1 \cdot i = i$

Step3: Rationalize the denominator

$\frac{1}{i} = \frac{1 \cdot i}{i \cdot i} = \frac{i}{i^2}$

Step4: Substitute $i^2=-1$

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

Answer:

$-i$