Category:Polar Form of Complex Number
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This category contains results about Polar Form of Complex Number.
Definitions specific to this category can be found in Definitions/Polar Form of Complex Number.
For any complex number $z = x + i y \ne 0$, let:
\(\ds r\) | \(=\) | \(\ds \cmod z = \sqrt {x^2 + y^2}\) | the modulus of $z$, and | |||||||||||
\(\ds \theta\) | \(=\) | \(\ds \arg z\) | 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 6 subcategories, out of 6 total.
A
C
D
E
P
Pages in category "Polar Form of Complex Number"
The following 5 pages are in this category, out of 5 total.