Complex analytic geometry

In mathematics, complex analytic geometry sometimes denotes the application of complex numbers to plane geometry.

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

Complex analytical geometry deals with solving geometrical problems, especially those 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.

Complex numbers can therefore be used to advantage to solve problems in elementary geometry. 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
• Complex manifold
• Riemann surface

References

• T. Andreescu and D. Andrica (2006) Complex Numbers From A To ...Z, Birkhäuser Verlag, ISBN 0-8176-4326-5 .
• P.S. Modenov (1981) Problems In Geometry, Mir Publishers, Moscow.
• Hans Schwerdtfeger (1962) Geometry of Complex Numbers, University of Toronto Press.
• Isaak Yaglom (1968) Complex Numbers in Geometry, translated by E. Primrose from 1963 Russian original, Academic Press, N.Y.

External links

• Complex Numbers and Geometry (Important formulas and links to applications)

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