Complex geometry

Complex analytical geometry deals with solving geometrical problems, especially involving angles, by means of complex algebra. Using Euler's formula,

<math>e^{i\theta}=\cos(\theta)+i\sin(\theta),\quad</math>

it is possible to represent any rotation as a complex number.

Rather than represent a point in the plane as a pair of Cartesian coordinates, it can simply be represented as a complex number, which in turn can be written in either rectangular or polar form.

Complex numbers can thus be used to solve problems in elementary geometry[?] in simple and clear way. This method is sometimes used in the advanced high-school mathematics, since it allows schoolchildren to write down angle relations in terms of simple formulas.

See also

• Conformal map