Be realistic

Algebra Level 3

Let \(f\) be a function defined for all complex numbers \(z\) as \(f(z)=z^2-2z+2\). Also let \(\text{Img}(z)\) denote the imaginary part of \(z\) and \(\text{Re}(z)\) denote the real part of \(z\).

If a complex number \(z\) is randomly selected such that \(\text{Re}(z)\in\{1,2,3,4\}\) and \(\text{Img}(z)\in\{1,2,3,4,5,6\}\), then the probability that \(f(z)\) is real is \(\frac{a}{b}\), where \(a\) and \(b\) are coprime, positive integers. Find \(a+b\).

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