Quiz3solns - 1 e-i 4 = e cos (- 4 ) + ie sin (- 4 ) = e 2 2...

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Quiz 3 Solutions Math 322, Fall 2009 September, 11 2009. NAME: Instructor: Bole Yang, Erica McEvoy Please show ALL of your work. 1. Find the principal value of Ln ( z ) when z =2 i. Rewrite z into polar form, so that z =2 e i ( π 2 +2 πn ) . Then Ln ( z )= ln ( r )+ iArg ( z )= ln (2) + i π 2 . (Since Arg (2 i )= π 2 ). 2. Consider the following complex number z =1 - π 4 i. (a) Write e z in the form u + iv . Use Euler’s formula to simplify e z : e 1 - π 4 i = e
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Unformatted text preview: 1 e-i 4 = e cos (- 4 ) + ie sin (- 4 ) = e 2 2 + ie 2 2 . So u = e 2 2 and v = e 2 2 . MATH 322. QUIZ 2 2 (b) Find | e z | . The modulus is just u 2 + v 2 = ( e 2 2 ) 2 + ( e 2 2 ) 2 = e 2 = e ....
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This note was uploaded on 12/01/2009 for the course MATH 322 taught by Professor Staff during the Fall '08 term at University of Arizona- Tucson.

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Quiz3solns - 1 e-i 4 = e cos (- 4 ) + ie sin (- 4 ) = e 2 2...

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