Question

compute ( i^{-95} ).

Explanation:

Step1: Rewrite negative exponent

$i^{-95} = \frac{1}{i^{95}}$

Step2: Find remainder of 95/4

$95 = 4\times23 + 3$, so $i^{95}=i^3$

Step3: Simplify $i^3$

$i^3 = i^2 \times i = -1 \times i = -i$

Step4: Rationalize the fraction

$\frac{1}{-i} = \frac{1 \times i}{-i \times i} = \frac{i}{-i^2} = \frac{i}{-(-1)} = i$

Answer:

$i$