(Complex Number)
(Complex Number)
Line 2: Line 2:
  
  
Complex Numbers are numbers that can be written in the form of: <math> A + Bi </math>
+
Complex Numbers are numbers that can be written in the form of: <math> A + Bj </math>
  
 
Below is a graph of the imaginary plane that will help visualize what this means.
 
Below is a graph of the imaginary plane that will help visualize what this means.
Line 11: Line 11:
  
 
B represents the imaginary part of the complex number.
 
B represents the imaginary part of the complex number.
 +
 +
Both A and B must be real numbers.
 +
 +
Fact:  Complex numbers are ONLY EQUAL if and only if the real coefficients are equal.
 +
Ex.
 +
 +
            A + Bj = C + Dj  A = C  B = D
 +
 +
                  5 + 3j =/= 5 + 2j
 +
 +
==Polar Form==
 +
 +
              Z = cos(θ) + j*sin(θ)
 +
 +
or written exponentially
 +
 +
              Z = e^(j*θ)
 +
 +
Converting to or from Polar Form.  Just remember these 3 easy equations.
 +
               
 +
                    x = r*cos(θ)
 +
                    y = r*sin(θ)
 +
                    r = sqrt(x^2 + y^2)
 +
 +
(having trouble with LaTeX.  Anyone is welcome to clean these up.)

Revision as of 14:19, 4 September 2008

Complex Number

Complex Numbers are numbers that can be written in the form of: $ A + Bj $

Below is a graph of the imaginary plane that will help visualize what this means.

ComplexNumber ECE301Fall2008mboutin.png

A represents the real part of the complex number.

B represents the imaginary part of the complex number.

Both A and B must be real numbers.

Fact: Complex numbers are ONLY EQUAL if and only if the real coefficients are equal. Ex.

            A + Bj = C + Dj   A = C  B = D 
                  5 + 3j =/= 5 + 2j

Polar Form

              Z = cos(θ) + j*sin(θ)

or written exponentially

              Z = e^(j*θ)

Converting to or from Polar Form. Just remember these 3 easy equations.

                    x = r*cos(θ)
                    y = r*sin(θ)
                    r = sqrt(x^2 + y^2)

(having trouble with LaTeX. Anyone is welcome to clean these up.)

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett