Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Imaginary Numbers Homework -- Homework: Complex Numbers

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Advanced Algebra II: Activities and Homework"

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This module is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy BusbeeAs a part of collection: "Advanced Algebra II: Activities and Homework"

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Imaginary Numbers Homework -- Homework: Complex Numbers

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to complex numbers.

Exercise 1

( 3 + 7 i ) ( 4 + 7 i ) = (3+7i)(4+7i)=

Exercise 2

( 5 3 i ) + ( 5 3 i ) = (53i)+(53i)=

Exercise 3

2 ( 5 3 i ) = 2(53i)=

Exercise 4

( 5 3 i ) ( 2 + 0 i ) = (53i)(2+0i)=

Exercise 5

What is the complex conjugate of ( 5 3 i ) (53i)?

Exercise 6

What do you get when you multiply ( 5 3 i ) (53i) by its complex conjugate?

Exercise 7

What is the complex conjugate of 7?

Exercise 8

What do you get when you multiply 7 by its complex conjugate?

Exercise 9

What is the complex conjugate of 2 i 2i?

Exercise 10

What do you get when you multiply 2 i 2i by its complex conjugate?

Exercise 11

What is the complex conjugate of ( a + b i ) (a+bi)?

Exercise 12

What do you get when you multiply ( a + b i ) (a+bi) by its complex conjugate?

Exercise 13

I’m thinking of a complex number zz. When I multiply it by its complex conjugate (designated as z *z*) the answer is 25.

  • a. What might z z be?
  • b. Test it, and make sure it works—that is, that ( z ) ( z * ) = 25 (z)(z*)=25!

Exercise 14

I’m thinking of a different complex number zz. When I multiply it by its complex conjugate, the answer is 3 + 2 i 3+2i.

  • a. What might z z be?
  • b. Test it, and make sure it works—that is, that ( z ) ( z * ) = 3 + 2 i (z)(z*)=3+2i!

Exercise 15

Solve for x x and y y: x 2 + 2 x 2 i + 4 y + 40 y i = 7 2 i x 2 +2 x 2 i+4y+40yi=72i

Exercise 16

Finally, a bit more exercise with rational expressions. We’re going to take one problem and solve it two different ways. The problem is 32+i7i3+4i32+i7i3+4i size 12{ { {3} over {2+i} } - { {7i} over {3+4i} } } {}. The final answer, of course, must be in the form a + b i a+bi.

  • a. Here is one way to solve it: the common denominator is ( 2 + i ) ( 3 + 4 i ) (2+i)(3+4i). Put both fractions over the common denominator and combine them. Then, take the resulting fraction, and simplify it into a + b i a+bi form.
  • b. Here is a completely different way to solve the same problem. Take the two fractions we are subtracting and simplify them both into a + b i a+bi form, and then subtract.
  • c. Did you get the same answer? (If not, something went wrong…) Which way was easier?

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks