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<math>|x + iy| = \sqrt{x^2 + y^2}</math> | <math>|x + iy| = \sqrt{x^2 + y^2}</math> | ||
| + | |||
In exponential form for <math>|z|</math> | In exponential form for <math>|z|</math> | ||
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== Basics == | == Basics == | ||
| − | <math>|z|^2</math> of <math>|z|</math> is known as the '''Absolute Square'''. | + | *<math>|z|^2</math> of <math>|z|</math> is known as the '''Absolute Square'''. |
| − | <math>\frac{|Ae^{i\phi}|}{|Be^{i\phi}|} = \frac{A}{B}\frac{e^i\phi}{e^i\phi}</math> | + | |
| + | *<math>\frac{|Ae^{i\phi}|}{|Be^{i\phi}|} = \frac{A}{B}\frac{|e^{i\phi}|}{|e^{i\phi}|} = \frac{A}{B}</math> | ||
| + | |||
| + | |||
| + | *<math>|\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{A}{B}|e^{i(\phi-\phi)}| = \frac{A}{B}</math> | ||
| + | |||
| + | |||
| + | *<math>|\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{|Ae^{i\phi}|}{|Be^{i\phi}|}</math> | ||
Revision as of 19:12, 4 September 2008
Complex Modulus
Complex Modulus, also known as the "Norm" of a complex number, is represented as $ |z| $.
$ |x + iy| = \sqrt{x^2 + y^2} $
In exponential form for $ |z| $
$ |re^{i\phi}| = r $
(This format is used when dealing with Phasors)
Basics
- $ |z|^2 $ of $ |z| $ is known as the Absolute Square.
- $ \frac{|Ae^{i\phi}|}{|Be^{i\phi}|} = \frac{A}{B}\frac{|e^{i\phi}|}{|e^{i\phi}|} = \frac{A}{B} $
- $ |\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{A}{B}|e^{i(\phi-\phi)}| = \frac{A}{B} $
- $ |\frac{Ae^{i\phi}}{Be^{i\phi}}| = \frac{|Ae^{i\phi}|}{|Be^{i\phi}|} $
