2002 AIME I Problems/Problem 12

Problem

Let $F(z)=\dfrac{z+1}{z-1}$ for all complex numbers $z\neq 1$ , and let $z_n=F(z_{n-1})$ for all positive integers $n$ . Given that $z_0=\dfrac{1}{137}+i$ and $z_{2002}=a+bi$ , where $a$ and $b$ are real numbers, find $a+b$ .

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2002 AIME I Problems/Problem 12

Problem

Solution

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