# 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 \(i^2=-1\).