Category:Definitions/Polar Form of Complex Number

This category contains definitions related to Polar Form of Complex Number.
Related results can be found in Category:Polar Form of Complex Number.

For any complex number $z = x + i y \ne 0$, let:

$\ds r$

$=$

$\ds \cmod z = \sqrt {x^2 + y^2}$

$\ds \theta$

$=$

$\ds \arg z$

the argument of $z$ (the angle which $z$ yields with the real line)

where $x, y \in \R$.

From the definition of $\arg z$:

$(1): \quad \dfrac x r = \cos \theta$

$(2): \quad \dfrac y r = \sin \theta$

which implies that:

$x = r \cos \theta$

$y = r \sin \theta$

which in turn means that any number $z = x + i y \ne 0$ can be written as:

$z = x + i y = r \paren {\cos \theta + i \sin \theta}$

The pair $\polar {r, \theta}$ is called the polar form of the complex number $z \ne 0$.

The number $z = 0 + 0 i$ is defined as $\polar {0, 0}$.

Subcategories

This category has the following 2 subcategories, out of 2 total.

The following 8 pages are in this category, out of 8 total.