PS1Solns

PS1Solns - UCSB Fall 2007 ECE 130A: Solutions to Problem...

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Unformatted text preview: UCSB Fall 2007 ECE 130A: Solutions to Problem Set 1 Problem 1 1 . 48 ( b ) z 2 = x + jy = r = x = r , y = 0 . 1 . 48 ( c ) z 3 = x + jy = r e j ( + ) = r e j e j x + jy = r e j ( cos ( ) + jsin ( )) =- r e j =- r ( cos ( ) + jsin ( )) x =- r cos , y =- r sin 1 . 48 ( d ) z 4 = x + jy = r e j (- + ) = r e- j e j x + jy = r e- j (- 1) =- r ( cos ( )- jsin ( )) x =- r cos , y = r sin Figure 1: r = 2 , = 4 Figure 2: r = 2 , = 2 Problem 2 1 . 49 ( b ) z 1 =- 5 = 5 e j r = 5 , = . 1 . 49 ( d ) z 2 = 3 + j 4; r = p 3 2 + 4 2 = 5 = arctan( 4 3 ) = 0 . 9273 radians = 53 . 13 degrees z 2 = 5 e j . 9273 1 . 49 ( f ) z 3 = (1 + j ) 5 , 1 + j = ( p 1 2 + 1 2 ) e j (arctan( 1 1 )) = 2 e j 4 z 3 = ( 2 e j 4 ) 5 = 4 2 e j 5 4 r = 4 2 , = 5 4 = 225 degrees Figure 3: Complex numbers in polar form (Problem 2) Problem 3 1 . 3 ( a ) x 1 ( t ) = e- 2 t u ( t ) E = R - ( e- 2 t u ( t )) 2 dt =...
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This note was uploaded on 08/06/2008 for the course ECE 130A taught by Professor Madhow during the Fall '07 term at UCSB.

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PS1Solns - UCSB Fall 2007 ECE 130A: Solutions to Problem...

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