Question

compute ( i^{-22} ).

Explanation:

Step1: Rewrite negative exponent

$i^{-22} = \frac{1}{i^{22}}$

Step2: Simplify $i^{22}$ using cycle of 4

$i^{22} = i^{4\times5 + 2} = (i^4)^5 \times i^2$
Since $i^4=1$ and $i^2=-1$, substitute:
$(1)^5 \times (-1) = -1$

Step3: Compute final value

$\frac{1}{i^{22}} = \frac{1}{-1} = -1$

Answer:

$-1$