(New page: == Definition of a Complex Number == The standard equation for complex numbers is: <math>a + bj = c</math> The <math>a</math> in the equation real part, and the <math>bj</math...) |
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<math>a + bj = c</math> | <math>a + bj = c</math> | ||
| − | The <math>a</math> in the equation real part, and the <math>bj</math> in | + | The <math>a</math> in the equation is the real part, and the <math>bj</math> in |
the equation is the imaginary part. | the equation is the imaginary part. | ||
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== Examples == | == Examples == | ||
| + | |||
| + | '''<math>j = \sqrt-1</math>''' | ||
| + | |||
| + | '''<math>j^2 = -1</math>''' | ||
| + | |||
| + | '''<math>j^3 = -j</math>''' | ||
| + | |||
| + | '''<math>j^4 = 1</math>''' | ||
| + | |||
| + | '''<math>8 + 3j + 12 - j = 20 + 2j</math>''' | ||
| + | |||
| + | '''<math>3j (4 - 6j) = 18 + 12j</math>''' | ||
| + | |||
| + | '''<math>(-2 + 4j) (1 - 2j) = -2 + 8j + 8 = 6 + 8j</math>''' | ||
| + | |||
| + | == Source == | ||
| + | |||
| + | Signals & Systems 2nd Edition Authors: S. Hamid Nawab, Alan V. Oppenheim, Alan S. Willsky | ||
Latest revision as of 12:12, 4 September 2008
Definition of a Complex Number
The standard equation for complex numbers is:
$ a + bj = c $
The $ a $ in the equation is the real part, and the $ bj $ in the equation is the imaginary part.
Some examples are listed below.
Examples
$ j = \sqrt-1 $
$ j^2 = -1 $
$ j^3 = -j $
$ j^4 = 1 $
$ 8 + 3j + 12 - j = 20 + 2j $
$ 3j (4 - 6j) = 18 + 12j $
$ (-2 + 4j) (1 - 2j) = -2 + 8j + 8 = 6 + 8j $
Source
Signals & Systems 2nd Edition Authors: S. Hamid Nawab, Alan V. Oppenheim, Alan S. Willsky
