Category:Examples of Use of Equation for Line through Two Points in Complex Plane
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This category contains examples of use of Equation for Line through Two Points in Complex Plane.
Let $z_1, z_2 \in \C$ be complex numbers.
Let $L$ be a straight line through $z_1$ and $z_2$ in the complex plane.
Formulation 1
$L$ can be expressed by the equation:
- $\map \arg {\dfrac {z - z_1} {z_2 - z_1} } = 0$
Parametric Form $1$
$L$ can be expressed by the equation:
- $z = z_1 + t \paren {z_2 - z_1}$
or:
- $z = \paren {1 - t} z_1 + t z_2$
This form of $L$ is known as the parametric form, where $t$ is the parameter.
Parametric Form $2$
$L$ can be expressed by the equations:
\(\ds x - x_1\) | \(=\) | \(\ds t \paren {x_2 - x_1}\) | ||||||||||||
\(\ds y - y_1\) | \(=\) | \(\ds t \paren {y_2 - y_1}\) |
These are the parametric equations of $L$, where $t$ is the parameter.
Symmetric Form
$L$ can be expressed by the equation:
- $z = \dfrac {m z_1 + n z_2} {m + n}$
This form of $L$ is known as the symmetric form.
Pages in category "Examples of Use of Equation for Line through Two Points in Complex Plane"
The following 5 pages are in this category, out of 5 total.
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- Equation for Line through Two Points in Complex Plane/Examples
- Equation for Line through Two Points in Complex Plane/Examples/2+i, 3-2i
- Equation for Line through Two Points in Complex Plane/Examples/2+i, 3-2i/Parametric Form 1
- Equation for Line through Two Points in Complex Plane/Examples/2+i, 3-2i/Parametric Form 2
- Equation for Line through Two Points in Complex Plane/Examples/2+i, 3-2i/Standard Form