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== Definition == | == Definition == | ||
− | + | 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. | ||
== Addition == | == Addition == | ||
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== 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 == |
Revision as of 12:13, 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)