1. (8 points) Section 3.1 a. If etz E IR, find all possible values of z. b. If er is purely imaginary (can be written in the form of iy, y is non-zero real number), find all possible values of z. 2. (8 points) Section 3.1 Write le5z+3i+2| and leiz | in terms of x, y, where z = x + iy, x, y E IR and then show that le 52 + 32+2 + eiz ? | 0, there exist a z such that | sin z| > M. c. Solve the equation cos z = 3. d. For one root of (choose any root you wish) the above equation, verify that sin z + cos z = 1. 4. (12 points) Sections 3.1-3.2 Solve each of the following for z E C. Do not use any formula for inverse functions in Section 3.7. a. sin z = 0. b. tan Tz = 1. c. 1 + ezz = 0