(New page: ==Norm and Agrument of a Complex Number== For any complex number :<math>z = x + iy\,</math> The '''norm''' (absolute value) of <math>z\,</math> is given by :<math> |z| = \sqrt{x^2+y^2}...) |
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:<math>z = x + iy\,</math> | :<math>z = x + iy\,</math> | ||
| − | The '''norm''' (absolute value) of <math>z\,</math> is given by | + | The '''norm''' (absolute value) of <math>z\,</math> is given by (<span style="color:red"> see important comment on [[HW1.3_David_Record_-_Magnitude_of_a_Complex_Number_ECE301Fall2008mboutin|this page]] regarding using the term "absolute value" only for real numbers</span>) |
:<math> |z| = \sqrt{x^2+y^2}</math> | :<math> |z| = \sqrt{x^2+y^2}</math> | ||
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The '''argument''' of <math>z\,</math> is given by | The '''argument''' of <math>z\,</math> is given by | ||
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:<math> z = x + iy = r(\cos \phi + i \sin \phi ) = r e^i\phi\,</math> | :<math> z = x + iy = r(\cos \phi + i \sin \phi ) = r e^i\phi\,</math> | ||
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| + | [[Main_Page_ECE301Fall2008mboutin|Back to ECE301 Fall 2008 Prof. Boutin]] | ||
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Revision as of 16:40, 4 January 2011
Norm and Agrument of a Complex Number
For any complex number
- $ z = x + iy\, $
The norm (absolute value) of $ z\, $ is given by ( see important comment on this page regarding using the term "absolute value" only for real numbers)
- $ |z| = \sqrt{x^2+y^2} $
The argument of $ z\, $ is given by
- $ \phi = arctan (y/x)\, $
Conversion from Cartesian to Polar Form
- $ x = r\cos \phi\, $
- $ y = \sin \phi\, $
- $ z = x + iy = r(\cos \phi + i \sin \phi ) = r e^i\phi\, $
Back to ECE301 Fall 2008 Prof. Boutin
