exam_1_m3364_summer_2011_v1_0

exam_1_m3364_summer_2011_v1_0 - e it + i for 0 6 t 6 2 ....

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Exam 1: Math 3364 Summer 2011 Problem 1. (10) Write the following complex numbers in the form x + iy . (a) (5) z = (2 + i ) / ( - 1 + 3 i ). (b) (5) z = i 3 ( i + 1) 2 . Problem 2. (15) Let z = (1 - i ) / (1 + i ). (a) (3) Write z in the form x + iy . (b) (3 each) Find z , Arg( z ), and | z | . (c) (3) Write z in the form re . Problem 3. (10) (a) (5) Write (1 + i ) 6 in the form re . (b) (5) Write z = e 5+ i ( π/ 2) e 3+ i ( π/ 4) in the form x + iy . Problem 4. (10) Sketch the curve z ( t ) = 2
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Unformatted text preview: e it + i for 0 6 t 6 2 . Problem 5. (10) Find all of the solutions to the equation z 4 = 16 i . Problem 6. (10) Let S be the set S = { z : | Im( z ) | > 1 } . (a) (5) Sketch S . (b) (5) State whether or not S is a domain. Problem 7. (10) Prove that if Re( z ) > 0, then Re(1 /z ) > 0. 1...
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