Question

Simplify i^22
1
–1
–i
i

Answer 1

-1

Answer 2

\[i^{22} = {(i^{2})}^{11} = (-1)^{11} = -1\]

Answer 3

(i^2)^11=(-1)^11=-1

Answer 4

I prefer this one:
\[i^2 = -1 \implies i^4 = (-1)^2 = 1\]\[i^{22} = i^{4\cdot 5}\cdot i^2= (i^4)^5 \cdot i^2 = 1^5\cdot -1 = -1\]