Domain of the analytic function

Question

Determine the domains where the following functions are analytic

i- f(z) = Log(-i+z). ii- g(z) = 1/(z^3 - 8i)

Answer 1

I graphed these:

i has negative slope of -0.532, and crosses x-axis at 1.532

ii has a vertical asymptote at x=2, crosses the x-axis at (0,0), and has a maximum at (-1.587, -0.132) and approaches y = 0 as x↔0 on both sides,