College Algebra Complex Numbers
Basic Definitions and Graphical Representation of Complex Numbers Concepts 1

|  |  | Definition 1 |  |
. |
A complex number, z, is a number of the form z = x+iy where x and y are real numbers and . Note: i2 = -1.

|  |  | Definition 2 |  |
. |
For the complex number z=x+iy, the real numbers x and y are known as the real and imaginary parts of z , respectively, and denoted Re z=x, Im z=y.

|  |  | Definition 3 |  |
. |
Two complex numbers z1=x1+iy1 and z2 = x2+iy2 are defined to be equal if and only if their real parts are equal and their imaginary parts are equal; that is, z1 =z2 if and only if x1= x2 and y1= y2.

Consequence. If the complex number x+iy=0, then x=0 and y=0.

|  |  | Definition 4 |  |
. |
Let z=x+iy. Then the complex conjugate of z, denoted , is defined as =x-iy.

Frequently used formulas

Copyright © 1998-2001 MathAid, LLC. All rights reserved.