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*<math>|1+2j| = \sqrt{5} </math> <br> | *<math>|1+2j| = \sqrt{5} </math> <br> | ||
*<math>|1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5}</math> | *<math>|1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5}</math> | ||
| − | *<math>e^{j60} = cos 60 +jsin 60</math> | + | *<math>e^{j60} = cos 60 + jsin 60</math> |
| + | *<math>e^{-j60} = cos 60 - jsin 60</math> | ||
Revision as of 09:41, 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} =\sqrt{5} $
- $ e^{j60} = cos 60 + jsin 60 $
- $ e^{-j60} = cos 60 - jsin 60 $
