# 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 $$a+b$$.

×