# OpenStax_CNX

You are here: Home » Content » The Complex Plane

### 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?

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

#### 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.
• Rice Digital Scholarship

This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Intro to Digital Signal Processing"

Click the "Rice Digital Scholarship" link to see all content affiliated with them.

### Recently Viewed

This feature requires Javascript to be enabled.

# The Complex Plane

Module by: Michael Haag. E-mail the author

Summary: (Blank Abstract)

## Complex Plane

The complex plane provides a way to express complex numbers graphically. Any complex number can be expressed as a point on the complex plane. Before looking over the rest of this module, one should be very familiar with complex numbers. Please refer to the complex number module for an explanation or review of these numbers.

Definition 1: Complex Plane
A two-dimensional graph where the horizontal axis maps the real part and the vertical axis maps the imaginary part of any complex number or function.

### Rectangular Coordinates

Similar to the Cartesian plane, the complex plane allows one to plot ordered pairs of the form a b a b , where aa and bb are real numbers that describe a unique complex number through the following general form:

z=a+ib z a b
(1)
This form is referred to as the rectangular coordinate.

### Polar Form

The complex plane can also be used to plot complex numbers that are in polar form. Rather than using aa and bb, the polar coordinates use rr and θθ in their ordered pairs. The rr is the distance from the origin to the complex number and θθ is the angle of the complex number relative to the positive, real axis. Look at the figure above to see these variables displayed on the complex plane. The general form for polar numbers is as follows: reiθ r θ

As a reminder, the following equations show the conversion between polar and rectangle coordinates:

r=a2+b2 r a 2 b 2
(2)
θ=arctanba θ b a
(3)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

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?

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