Answer
For any positive power, $n$, of $i$, the simplified form of $i^n$ will be $i^2$ raised to the Quotient times $i$ raised to the Remainder of the positive power, $n$, when divided by 2 respectively.
Work Step by Step
For any positive power, $n$, of $i$,
let $n = 2Q + R$, where, $Q$ = Quotient and $R$ = Remainder of $n$ when divided by 2 respectively.
For $i^n$,
$i^n$ = $i^{2Q+R}$
= $i^{2Q} \cdot i^R$ (Rule of Exponents : Multiplication Rule)
= $(i^2)^Q \cdot i^R$ (Rule of Exponents : Power of a Power Rule)
So, for any positive power, $n$, of $i$, the simplified form of $i^n$ will be $i^2$ raised to the Quotient times $i$ raised to the Remainder of the positive power, $n$, when divided by 2 respectively.
