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Norm and Agrument of a Complex Number (HW1, ECE301, Fall 2008)

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\, $

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