{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1solns.220.06

hw1solns.220.06 - 1 ECE 220 HOMEWORK 1 SOLUTION I PROBLEM...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ECE 220 HOMEWORK 1 SOLUTION I. PROBLEM 1 (a) See Fig1. Re(z) Im(z) z=0+j2 z=-1+j z=-j Fig. 1. Plots for Problem 1 (b) z = 0 + j 2 = 2 ∠ π/ 2 = 2 ∠- 3 π/ 2 z = (- 1 , 1) = √ 2 ∠ 3 π/ 4 = √ 2 ∠- 5 π/ 4 z = (0 ,- 1) = 1 ∠ 3 π/ 2 = 1 ∠- π/ 2 . (c) z = 0 + j 2 ⇒ √ z = √ 2 ∠ π/ 4 or √ 2 ∠- 3 π/ 4 z = (- 1 , 1) ⇒ √ z = 2 1 / 4 ∠ 3 π/ 8 or 2 1 / 4 ∠- 5 π/ 8 z = (0 ,- 1) ⇒ √ z = 1 ∠ 3 π/ 4 or 1 ∠- π/ 4 . II. PROBLEM 2 (a) See Fig2. (b) z = √ 2 e j 3 π 4 = √ 2(- √ 2 / 2 + j √ 2 / 2) =- 1 + j z = 3 e- j π 2 = 3(0- j ) =- 3 j . III. PROBLEM 3 (a) j 3 = j 2 j =- j = (0 , 1) (b) e j ( π +2 πm ) = cos( π + 2 πm ) + j sin( π + 2 πm ) = cos π + j sin π =- 1 = (- 1 , 0) for all m . (c) j 2 n = ( j 2 ) n = (- 1) n = (- 1 , 0) if n is odd ; (1 , 0) if n is even . (d) j 1 / 2 = ( e j π 2 ) 1 / 2 = e j π 4 or e- j 3 π 4 = ( √ 2 / 2 , √ 2 / 2) or (- √ 2 / 2 ,- √ 2 / 2) . 2 Re(z) Im(z) z = √ 2 e j (3 π/ 4) z = 3 e- j ( π/...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

hw1solns.220.06 - 1 ECE 220 HOMEWORK 1 SOLUTION I PROBLEM...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online