DOC PREVIEW
Purdue ECE 20100 - HW 30

This preview shows page 1 out of 3 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Homework 30ECE201: Linear Circuit AnalysisDue in class: Friday, November 11, 2011Question 1Add the complex numbers and . Express your answer (a) in real and imaginary parts, and (b) as a magnitude and phase. Draw z1, z2 and z1 + z2 on the complex plane. Label the real part, the imaginary part, and magnitude and the phase of z1 + z2.Hints (you should be able to solve the previous problem without the hints. Please refrain from reading the hints unless you have invested significant effort). You are not required to write up answers for the questions in this hint.1. The basic formula for complex number representation for real values is the Euler’s formula: . This formula allows you to transfer a complex number in polar form into or real and imaginary parts. You need to memorize it for the duration of ECE 201.2. θ is typically expressed in radians. Notice that π in radians equals to 180°. 3. A complex number corresponds to a point in a “complex plane” where the x-axis is for the real part of the complex number and the y-axis is for the imaginary part.4. The addition of two complex numbers follow the similar rule as you might have learned in vector algebra.Question 2Multiply the complex numbers z1 = 12-16 j and z2 = –1+0.75j. Express your answer (a) in real and imaginary parts, and (b) as a magnitude and phase. (c) Compare to . (d) What is the relationship between the phase of z1, the phase of z2, and the phase of z1z2?Hints (you should be able to solve the previous problem without the hints. Please refrain from reading the hints unless you have invested significant effort). You are not required to write up answers for the questions in this hint.1. The best way to convert a complex number in real and imaginary part to polar form is to place the number in the complex plane. In this way you will visually find out the phase, θ, with no ambiguity. 2. You can then use θ = tan-1(b/a) to find the value of , given that you know what quadrant the complex number is in.3. The absolution value of a complex number, for example |z1|, is the distance from the origin to the point corresponding to the complex number, i.e. z1, in the complex plane. If z = a + jb, then .Question 3For z1 and z2 given in Question 2, determine z1/z2. Express your answer (a) in real and imaginary parts, and (b) as a magnitude and phase. (c) Compare and to . (d) What is the relationship between the phase of z1, the phase of z2, and the phase of z1/z2?Hints (you should be able to solve the previous problem without the hints. Please refrain from reading the hints unless you have invested significant effort). You are not required to write up answers for the questions in this hint.1. This question introduces a very important concept, conjugate of a complex number. The definition is very simple: if z = a + jb, then its conjugate, z* = a – jb. You need to memorize this definition and be able to apply it in ECE 201.2. Immediately following hint #3 in Question 2, we found that the absolution value of a complex number and its conjugate are equal: |z| = |z*|. Can you prove it?3. What is the product of a complex number and its conjugate?4. If the denominator of a fraction is a complex number in real and imaginary part, one should multiply its conjugate to both the numerator and denominator. The denominator will become a real number as it is multiplied by its conjugate. This would allow you to further simplify the


View Full Document

Purdue ECE 20100 - HW 30

Documents in this Course
Quiz10

Quiz10

2 pages

Quiz7

Quiz7

3 pages

lect40

lect40

11 pages

lect39

lect39

14 pages

lect38

lect38

12 pages

lect37

lect37

12 pages

lect36

lect36

13 pages

lect35

lect35

8 pages

lect34

lect34

5 pages

lect33

lect33

8 pages

lect32

lect32

8 pages

lect31

lect31

10 pages

lect30

lect30

11 pages

lect29

lect29

7 pages

lect28

lect28

10 pages

lect27

lect27

10 pages

lect26

lect26

13 pages

lect25

lect25

9 pages

lect24

lect24

12 pages

lect23

lect23

11 pages

lect22

lect22

8 pages

lect21

lect21

6 pages

lect20

lect20

6 pages

lect19

lect19

12 pages

lect18

lect18

7 pages

lect17

lect17

16 pages

lect16

lect16

12 pages

lect15

lect15

14 pages

lect14

lect14

9 pages

lect13

lect13

15 pages

lect12

lect12

13 pages

lect11

lect11

10 pages

lect10

lect10

14 pages

lect9

lect9

6 pages

lect8 (1)

lect8 (1)

11 pages

lect7 (1)

lect7 (1)

11 pages

lect6

lect6

8 pages

lect5

lect5

9 pages

lect4

lect4

12 pages

lect3

lect3

9 pages

lect2

lect2

14 pages

lect1

lect1

8 pages

HW40

HW40

2 pages

hw30

hw30

4 pages

hw29

hw29

3 pages

hw28

hw28

3 pages

hw27

hw27

2 pages

hw26

hw26

2 pages

HW24

HW24

7 pages

hw23

hw23

4 pages

HW22

HW22

3 pages

HW21

HW21

5 pages

HW20

HW20

5 pages

hw17

hw17

3 pages

hw13

hw13

3 pages

HW11

HW11

4 pages

HW10

HW10

6 pages

HW9

HW9

3 pages

HW9 (2)

HW9 (2)

3 pages

HW7

HW7

6 pages

HW6

HW6

3 pages

hw5

hw5

4 pages

HW5 (2)

HW5 (2)

2 pages

HW4

HW4

4 pages

HW4 (2)

HW4 (2)

2 pages

HW3

HW3

4 pages

HW3 (2)

HW3 (2)

2 pages

HW2

HW2

2 pages

HW1

HW1

3 pages

HW1 (2)

HW1 (2)

2 pages

hw_25

hw_25

6 pages

hw_24

hw_24

7 pages

hw_11

hw_11

4 pages

hw_10

hw_10

6 pages

hw_9

hw_9

3 pages

hw_8

hw_8

4 pages

hw_7

hw_7

6 pages

hw_6

hw_6

3 pages

HW 33

HW 33

2 pages

HW 32

HW 32

4 pages

HW 31

HW 31

2 pages

HW 29

HW 29

5 pages

HW 28

HW 28

2 pages

HW 27

HW 27

2 pages

HW 26

HW 26

2 pages

HW 23

HW 23

2 pages

HW 22

HW 22

2 pages

HW 21

HW 21

2 pages

HW 19

HW 19

2 pages

HW 18

HW 18

3 pages

HW 17

HW 17

3 pages

HW 16

HW 16

2 pages

HW 15

HW 15

2 pages

HW 14

HW 14

3 pages

HW 13

HW 13

3 pages

HW 12

HW 12

2 pages

HW 11

HW 11

2 pages

HW 10

HW 10

2 pages

HW 9

HW 9

3 pages

HW 8

HW 8

2 pages

HW 7

HW 7

2 pages

HW 6

HW 6

2 pages

HW 5

HW 5

3 pages

HW 4

HW 4

4 pages

HW 3

HW 3

2 pages

HW 2

HW 2

2 pages

fallo4

fallo4

10 pages

Exam3 S10

Exam3 S10

10 pages

exam2c

exam2c

4 pages

exam2a

exam2a

13 pages

ex4sp06

ex4sp06

23 pages

2007

2007

17 pages

2004ans

2004ans

7 pages

18

18

15 pages

16

16

19 pages

14

14

16 pages

11

11

17 pages

10

10

18 pages

9

9

14 pages

7

7

16 pages

6

6

17 pages

5

5

4 pages

4

4

15 pages

Load more
Download HW 30
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view HW 30 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view HW 30 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?