# Maximize real and imaginary parts

Algebra Level 5

Suppose $z = a + bi$, where $a$ and $b$ are integers and $i$ is the imaginary unit. We are given that $|1+iz| = |1-iz|$ and $|z - (13+15i)| < 17$. Find the largest possible value of $a+b$.

Details and assumptions

$i$ is the imaginary unit, where $i^2=-1$.

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