Mock AIME 2 2006-2007 Problems/Problem 4

Problem

Let $\displaystyle n$ be the smallest positive integer for which there exist positive real numbers $\displaystyle a$ and $\displaystyle b$ such that $\displaystyle (a+bi)^n=(a-bi)^n$ . Compute $\displaystyle \frac{b^2}{a^2}$ .

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Mock AIME 2 2006-2007 Problems/Problem 4

Problem