Complex variables

Please see the attached file for full problem description. --- 5. Write |exp (2z + i) | and | exp (iz2) | in terms of x and y. Then show that | exp (2z + i) + exp (iz2) | ≤ e2x + e-2xy. (exp means exponential function)

Complex variables

Please see the attached file for full problem description. --- 3. Show that (a) Log (1 + i)2 = 2 Log (1 + i) (b) Log (-1 + i)2 ≠ 2 Log (-1 + i).

Complex variables

Please see the attached file for full problem description. --- 5. Show that (a) the set of values of log(i1/2) is (n + ¼) π i (n = 0, ± 1, ±2, …) and that the same is true of (1/2)log i; (b) the set of values of log(i2) is not the same as the set of values of 2log i.

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.