Math 316 Complex Variables

Question

MATH 316 Complex Variables,

question in the picture above.

. Consider the following subsets of the complex plane: (a) (4 points) {z E C I Re(z2 + 1) = 0} (b) (4 points) {z 6 (Cl lz— 1| 3 2 and z 75 0} (c) (5 points) {z E (C | 2 7g 0 and — 7r/2 lt; Arg(z3) lt; 7r/2} Draw a picture of each of these subsets, and state (without proof) which of the following
conditions they satisfy: 0 bounded 0 open 0 closed 0 connected 0 a domain Math