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| − | Complex Numbers are numbers that can be written in the form of: <math> A + | + | 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. | ||
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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== | ||
| + | |||
| + | In Polar Form, we use radius and angle instead of the distances x and y. | ||
| + | r is the distance from the origin. | ||
| + | θ is the angle in degrees. | ||
| + | |||
| + | r*cos(θ) + j*r*sin(θ) | ||
| + | |||
| + | or written exponentially | ||
| + | |||
| + | r*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.) | ||
Latest revision as of 14:23, 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.
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
In Polar Form, we use radius and angle instead of the distances x and y. r is the distance from the origin. θ is the angle in degrees.
r*cos(θ) + j*r*sin(θ)
or written exponentially
r*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.)
