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== Definition == | == Definition == | ||
| − | + | <font size="3">A complex number is made up of two parts, a real part and an imaginary part. An example is | |
| + | |||
| + | <math>a+bi</math>, where <math>a</math> is the real part and <math>b</math> is the imaginary part.</font> | ||
== Addition == | == Addition == | ||
| − | + | <font size="3"><math>(a + bj) + (c + dj) = (a + c) + (b + d)j</math></font> | |
== Subtraction == | == Subtraction == | ||
| − | + | <font size="3"><math>(a + bj) - (c + dj) = (a - c) + (b - d)j</math></font> | |
== Multiplication == | == Multiplication == | ||
| − | + | <font size="3"><math>(a + bj)(c + dj) = (ac - bd) + (ad + bc)j</math></font> | |
== Division == | == Division == | ||
| − | + | <math>\frac{(a + bj)}{(c + dj)} = \frac{(a + bj)(c - dj)}{(c + dj)(c - dj)} = | |
| + | \frac{(a + bj)(c - dj)}{(c^2 - d^2)} = \frac{(ac + bd) + (bc - ad)j}{(c^2 - d^2)}</math> | ||
== Applications == | == Applications == | ||
| + | <font size="3">Applications include: | ||
| + | |||
| + | - Control Theory | ||
| + | |||
| + | - Fluid Flow | ||
| + | |||
| + | - Signal Processing | ||
| + | |||
| + | - Quantum Mechanics | ||
| + | |||
| + | - Relativity | ||
| − | + | - Fractals (my personal favorite)</font> | |
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== Sources == | == Sources == | ||
http://en.wikipedia.org/wiki/Complex_numbers | http://en.wikipedia.org/wiki/Complex_numbers | ||
Latest revision as of 13:23, 4 September 2008
Definition
A complex number is made up of two parts, a real part and an imaginary part. An example is
$ a+bi $, where $ a $ is the real part and $ b $ is the imaginary part.
Addition
$ (a + bj) + (c + dj) = (a + c) + (b + d)j $
Subtraction
$ (a + bj) - (c + dj) = (a - c) + (b - d)j $
Multiplication
$ (a + bj)(c + dj) = (ac - bd) + (ad + bc)j $
Division
$ \frac{(a + bj)}{(c + dj)} = \frac{(a + bj)(c - dj)}{(c + dj)(c - dj)} = \frac{(a + bj)(c - dj)}{(c^2 - d^2)} = \frac{(ac + bd) + (bc - ad)j}{(c^2 - d^2)} $
Applications
Applications include:
- Control Theory
- Fluid Flow
- Signal Processing
- Quantum Mechanics
- Relativity
- Fractals (my personal favorite)
