combinatorics - Simplify the Expression $sum _{ k=0 }^{ n }{ binom{n}{k}}i^{k}3^{k-n} $

I should simplify the following expression (for a complex number):
$$\sum _{ k=0 }^{ n }{ \binom{n}{k}}i^{k}3^{k-n} $$

The solution is $(i+\frac{1}{3})^n$,but i don't quite get the steps. If would be nice if someone could explain.

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The Binomial Theorem:
$(x+y)^{n}=\sum_{k=0}^{n}\binom{n}{k}x^{n-k}y^{k}$

Answer

$$
\sum_{k=0}^n \binom{n}{k}i^k 3^{k-n}

= \sum_{k=0}^n \binom{n}{k}i^k \left(3^{-1}\right)^{n-k}
= \sum_{k=0}^n \binom{n}{k}i^k \left(1/3\right)^{n-k}
= (i+1/3)^n
$$