Hello, I have complex variables questions.

I need your help.

Thank you so much.

Q1:

[5 pts] Let C be any simple Closed contour, described in the negative sense in the complex plane, and write 5433 g(z) = jamds. Find the value of g(z) for the following two cases. (i) z is inside of the contour C; (ii) 2 is outside of the contour C. (6 pts] Let C denote the positively oriented unit circle z = 1 about the origin. (a) Suppose f (z) is the principal branch -5/4 _ e- Logz (|z) > 0, -T 0,0