Question

compute ( i^{-48} ).

Explanation:

Step1: Recall $i$ cycle property

$i^4 = 1$, $i^{-n} = \frac{1}{i^n}$

Step2: Rewrite exponent as multiple of 4

$i^{-48} = \frac{1}{i^{48}} = \frac{1}{(i^4)^{12}}$

Step3: Substitute $i^4=1$

$\frac{1}{(1)^{12}} = \frac{1}{1}$

Step4: Simplify the fraction

$\frac{1}{1} = 1$

Answer:

1