If $n$ is the smallest positive integer for which there exist positive real numbers $a$ and $b$ such that
\[(a + bi)^n = (a - bi)^n,\]compute $\frac{b}{a}.$The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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