# Category:Definitions/Polar Form of Complex Number

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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:

\(\displaystyle r\) | \(=\) | \(\displaystyle \cmod z = \sqrt {x^2 + y^2}\) | the modulus of $z$, and | ||||||||||

\(\displaystyle \theta\) | \(=\) | \(\displaystyle \arg z\) | 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.

## Pages in category "Definitions/Polar Form of Complex Number"

The following 4 pages are in this category, out of 4 total.