Let f be a function defined for all complex numbers z as f(z)=z2−2z+2. Also let Img(z) denote the imaginary part of z and Re(z) denote the real part of z.
If a complex number z is randomly selected such that Re(z)∈{1,2,3,4} and Img(z)∈{1,2,3,4,5,6}, then the probability that f(z) is real is ba, where a and b are coprime, positive integers. Find a+b.