## Encyclopedia > Complex geometry

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# Complex geometry

Complex analytical geometry deals with solving geometrical problems, especially involving angles, by means of complex algebra. Using Euler's formula,
$e^{i\theta}=\cos(\theta)+i\sin(\theta),\quad$
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.

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