Category:Examples of Polar Form of Complex Number
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This category contains examples of 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 $\polar {0, 0}$.
Pages in category "Examples of Polar Form of Complex Number"
The following 27 pages are in this category, out of 27 total.
P
- Polar Form of Complex Number/Examples
- Polar Form of Complex Number/Examples/-1
- Polar Form of Complex Number/Examples/-1 + root 3 i
- Polar Form of Complex Number/Examples/-2 root 3 - 2 i
- Polar Form of Complex Number/Examples/-3 - 4i
- Polar Form of Complex Number/Examples/-3i
- Polar Form of Complex Number/Examples/-4
- Polar Form of Complex Number/Examples/-5 + 5i
- Polar Form of Complex Number/Examples/-i
- Polar Form of Complex Number/Examples/-root 6 - root 2 i
- Polar Form of Complex Number/Examples/1 - 2i
- Polar Form of Complex Number/Examples/12 cis 90
- Polar Form of Complex Number/Examples/2 + 2 root 3 i
- Polar Form of Complex Number/Examples/2 + i
- Polar Form of Complex Number/Examples/2 - 2i
- Polar Form of Complex Number/Examples/2 cis -pi 4^-1
- Polar Form of Complex Number/Examples/2 cis 5 pi 4^-1
- Polar Form of Complex Number/Examples/2 root 2 + 2 root 2 i
- Polar Form of Complex Number/Examples/3 cis -2 pi 3^-1
- Polar Form of Complex Number/Examples/4 cis 3 pi 5^-1
- Polar Form of Complex Number/Examples/4 cis 315
- Polar Form of Complex Number/Examples/5 cis 7 pi 6^-1
- Polar Form of Complex Number/Examples/6 cis 135
- Polar Form of Complex Number/Examples/6 cis 240
- Polar Form of Complex Number/Examples/i
- Polar Form of Complex Number/Examples/root 2 i
- Polar Form of Complex Number/Examples/root 3 over 2 - 3 i over 2