I've self-learning of a complex analysis course. My first difficulties are in analytic functions. In that book, that I learning from, there is no even one example on how proving such problem, like in the title:
Prove that $w=\frac{\sqrt{z^2+z+1}}{z^2-3z+2}$ analytic on $|z|<1$
Could you direct me by providing a full solution of the above?
Thank you.