Maximize real and imaginary parts

Algebra Level 5

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

Details and assumptions

ii is the imaginary unit, where i2=1i^2=-1.

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