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Unformatted text preview: < e stands for real part of a complex number) 1 5. (10 Points) Determine real and imaginary parts of following complex number: (1 + j )-2011 (Hint: Use following formula and polar form representation of the com-plex number, i.e., 1 2 (1 + j ) = e j/ 4 ) (cos + j sin ) n = cos n + j sin n 6. (30 Points) By use of Eulers formula show that: (a) cos = 1- 2 2! + 4 4!- 6 6! +- - - - - - - - - - - - - sin = - 3 3! + 5 3!- 7 7! +- - - - - - - - - - - - - (b) 1 . Z e a sin b d = e a a 2 + b 2 ( a sin b-b cos b ) 2 . Z e a cos b d = e a a 2 + b 2 ( a cos b + b sin b ) (c) cos( A + B ) = cos A cos B-sin A sin B (Hint: e j = cos + j sin ) 2...
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This note was uploaded on 10/25/2011 for the course ELCT 321 taught by Professor Shin during the Spring '08 term at South Carolina.
- Spring '08