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Quiz3solns

# Quiz3solns - 1 e-i π 4 = e cos-π 4 ie sin-π 4 = e √ 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 π n ) . 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

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Unformatted text preview: 1 e-i π 4 = e cos (-π 4 ) + ie sin (-π 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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