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 $a+b$ .