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homework20110902

homework20110902 - z 5 = − 1 i √ 3 4 Find the real and...

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Math 417, Fall 2011 Exercise Set #1 Turn in: September 2 1. Solve a + i · b = (2 + i )(3 + 2 i ) (1 i ) for a and b . 2. Draw the graph in the complex plane of all z C satisfying a) ° ° ° ° z 1 z +2 ° ° ° ° 1. b) | z | 2 =im( z ). 3. a) Express the complex number w = 1+ i 3inpo larform . b) Find all solutions
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Unformatted text preview: z 5 = − 1 + i √ 3. 4. Find the real and imaginary parts of the functions: a) f ( z ) = z − 1 z + 2 b) exp(2 z + 3 i ) 5. Show that if a, b ∈ C satisfy | a | < 1 and | b | < 1, then | a − b | | 1 − ab | < 1. 1...
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