Let $f(z)=e^x + ie^{2y}$ where z=x+iy is a complex variable defined in the whole complex plane.
a)Where does f'(z) exist? b) Where is f(z) analytic?
Answer:
a) I used the Cauchy Riemann to test whether the function is holomorphic. i got $x=\log2 + 2y$
b) I am not sure how to check if f(z) is analytic??????