Question: cosz is analytic or not?
Answer: A function is called analytic when Cauchy-Riemann equations hold in an open set. ... So sin z is not analytic anywhere. Similarly cos z = cosxcosh y + isinxsinhy = u + iv, and the Cauchy-Riemann equations hold when z = nπ for n ∈ Z. Thus cosz is not analytic anywhere, for the same reason as above.