Hwk1_2006Fall - 2. A complex unction is defned by H ( z ) =...

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ECE 3337 Homework 1 Fall 2006 Due: September 11, 2006 (Jansen) September 12, 2006 (Kalatsky) 1. For the three complex variables defned by z 1 =5 - 2 j z 2 = 4(cos π/ 6+ j sin π/ 6) z 3 = - 1 2 2 e - jπ/ 4 , answer the ±ollowing questions: (a) Sketch, to scale, each o± the three variables in the z -plane. (b) Indicate ±or which o± the z ’s it is true that | z - j | > 0 . 5. (c) Express z 1 and z 2 in exponential ±orm. (d) Compute z 1 - z 3 , z 2 · z 3 , | z 1 /z 3 | , and | j - z 3 | . (e) Compute ( z 3 ) 1 / 3 and ln z 2 . (±) Compute and sketch (to scale) 1 /z 3 and its conjugate.
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Unformatted text preview: 2. A complex unction is defned by H ( z ) = ( z 3-1)( z 2-. 5 e j/ 4 ) z 2 + 2 z + 1 (a) Determine the zeros (i.e., the values o z or which H ( z ) = 0) and the poles (i.e., the values o z or which H ( z ) = ). (b) Determine whether H ( z ) is continuous or all z . (c) Compute lim z -1 H ( z ) 3. Compute the derivative o G ( z ) = ( z 2-. 5 e j/ 4 ) z-j . 1...
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This note was uploaded on 10/26/2011 for the course ECE 3337 taught by Professor Staff during the Fall '08 term at University of Houston.

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