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A complex number is defined as any number with both real and imaginary components. A few examples of this are below... | A complex number is defined as any number with both real and imaginary components. A few examples of this are below... | ||
| − | + | 1 + 2j | |
| + | 2 + 3j | ||
| + | |||
| + | Where 'j' is equal to the square root of negative one. To separate real and imaginary parts, the following convention is generally used. | ||
| + | |||
| + | Re(1+2j) = 1 | ||
| + | Im(1+2j) = 2 | ||
| + | |||
| + | Notice, the imaginary part of (1 + 2j) is only equal to the coefficient of the 'j term.' | ||
| + | |||
| + | == Examples With Imaginary Numbers == | ||
| + | |||
| + | A few imporant properties of imaginary numbers are shown below. | ||
| + | |||
| + | <math>j = sqrt(-1)</math> | ||
| + | |||
| + | <math>j^2 = -1 </math> | ||
| + | |||
| + | <math>j^3 = -j </math> | ||
| + | |||
| + | <math>j^4 = 1 </math> | ||
| + | |||
| + | As can be seen above, j^n is a repeating function. | ||
Latest revision as of 15:24, 5 September 2008
Complex Number Definition
A complex number is defined as any number with both real and imaginary components. A few examples of this are below...
1 + 2j 2 + 3j
Where 'j' is equal to the square root of negative one. To separate real and imaginary parts, the following convention is generally used.
Re(1+2j) = 1 Im(1+2j) = 2
Notice, the imaginary part of (1 + 2j) is only equal to the coefficient of the 'j term.'
Examples With Imaginary Numbers
A few imporant properties of imaginary numbers are shown below.
$ j = sqrt(-1) $
$ j^2 = -1 $
$ j^3 = -j $
$ j^4 = 1 $
As can be seen above, j^n is a repeating function.
