# Category:Geometry of Complex Plane

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This category contains results about Geometry of Complex Plane.

Because a complex number can be expressed as an ordered pair, we can plot the number $x + i y$ on the real number plane $\R^2$:

This representation is known as the **complex plane**.

### Real Axis

Complex numbers of the form $\tuple {x, 0}$, being wholly real, appear as points on the $x$-axis.

### Imaginary Axis

Complex numbers of the form $\tuple {0, y}$, being wholly imaginary, appear as points on the points on the $y$-axis.

This line is known as the **imaginary axis**.

## Subcategories

This category has the following 13 subcategories, out of 13 total.

### C

### E

## Pages in category "Geometry of Complex Plane"

The following 33 pages are in this category, out of 33 total.

### C

- Complex Multiplication as Geometrical Transformation
- Complex Numbers are Parallel iff Cross Product is Zero
- Complex Numbers are Perpendicular iff Dot Product is Zero
- Complex Roots of Unity are Vertices of Regular Polygon Inscribed in Circle
- Condition for Collinearity of Points in Complex Plane
- Condition for Complex Number to be in Right Half Plane
- Condition for Points in Complex Plane to form Isosceles Triangle
- Condition for Points in Complex Plane to form Parallelogram

### E

- Equation for Line through Two Points in Complex Plane
- Equation for Perpendicular Bisector of Two Points in Complex Plane
- Equation of Circle in Complex Plane
- Equation of Circular Arc in Complex Plane
- Equation of Ellipse in Complex Plane
- Equation of Hyperbola in Complex Plane
- Equation of Imaginary Axis in Complex Plane
- Equation of Line in Complex Plane
- Equation of Unit Circle in Complex Plane
- Equation relating Points of Parallelogram in Complex Plane