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== Some Operations == | == Some Operations == | ||
* <math>j^2 = -1</math> | * <math>j^2 = -1</math> | ||
| − | * <math>|a+bj| =\sqrt | + | * <math>|a+bj| =\sqrt{a^2+b^2}</math> |
* <math>|z| = |\overline z|</math> , where z is complex number | * <math>|z| = |\overline z|</math> , where z is complex number | ||
* '''Euler Equation''' : <math>e^{aj} = cos a + isin a</math> | * '''Euler Equation''' : <math>e^{aj} = cos a + isin a</math> | ||
| + | |||
| + | == Examples == | ||
| + | *<math>|1+2j| = \sqrt{1^2+2^2}</math> | ||
| + | *<math>|1+2j| = \sqrt{5} = |1-2j| = \sqrt{1^2+(-2)^2}</math> | ||
Revision as of 09:39, 1 September 2008
Definition
- the complex numbers are combinations of both real parts and imaginary parts, denoted i.
- These can be written a+bi, where a and b are real numbers.
Some Operations
- $ j^2 = -1 $
- $ |a+bj| =\sqrt{a^2+b^2} $
- $ |z| = |\overline z| $ , where z is complex number
- Euler Equation : $ e^{aj} = cos a + isin a $
Examples
- $ |1+2j| = \sqrt{1^2+2^2} $
- $ |1+2j| = \sqrt{5} = |1-2j| = \sqrt{1^2+(-2)^2} $
