Inversion in a unit circle is a mathematical operation that transforms points on a circle into their corresponding points on the opposite side of the circle. It is also known as circle inversion or reflection in a circle.
To perform inversion in a unit circle, the center of the circle is chosen as the inversion point. A point on the circle is then connected to the inversion point with a straight line. The point is then reflected along this line to its corresponding point on the opposite side of the circle.
The relationship between the original point and its inverted point is that they are equidistant from the inversion point. This means that the distance from the original point to the inversion point is equal to the distance from the inverted point to the inversion point.
Some properties of inversion in a unit circle include:
Inversion in a unit circle is used in various fields of mathematics, such as geometry, complex analysis, and number theory. It is particularly useful in solving problems involving circles, tangents, and power of a point. In complex analysis, inversion in a unit circle is used to transform circles and lines into other circles and lines, making it a powerful tool in solving complex functions and equations.