The problems are from complex variable class, 500 level in undergraduate.

The problems are from complex variable class. Please specify the terms that you use if necessary and explain each step of your solution. If there is anything unclear in the problem, please tell me. Thank you very much.

The problems are from complex variable class, 500 level in undergraduate.

The problems are from complex variable class. Please specify the terms that you use if necessary and explain each step of your solution. If there is anything unclear in the problem, please tell me. Thank you very much.

Complex Variable - 500 Level Undergraduate Class

By finding an antiderivative, evaluate each of these integrals, where the path is any contour between the indicated limite of intergration. (See attachment for full question)

Complex Variable - 500 Level Undergraduate Class.

Show that the integration from -1 to 1 z^i dz = ((1+e^-pi)/2)*(1-i)where zi denotes the principal branch... (See attachment for full question)

Complex Variable - 500 Level Undergraduate Class

Apply the Cauchy-Goursat theorem to show that... (See attachment for full question)