In mathematics, n-dimensional complex space is a multi-dimensional generalisation of the complex numbers, which have both real and imaginary parts or dimensions. The n-dimensional complex space can be seen as n cartesian products of the complex numbers with itself:
The n-dimensional complex space consists of ordered n-tuples of complex numbers, called coordinates:
The real and imaginary parts of a complex number may be treated as separate dimensions. With this interpretation, the space of n complex numbers can be seen as having dimensions represented by -tuples of real numbers. The two different interpretations can cause confusion about the dimension of a complex space.
The term "complex plane" can be confusing. It is sometimes used to denote , and sometimes to denote the space represented in the Argand diagram (with the Riemann sphere referred to as the "extended complex plane"). In the present context of , it is understood to denote .
- Djoric, M. & Okumura, M.; CR Submanifolds of Complex Projective Space, Springer 2010
- Edwards, L.; Projective geometry (2nd Ed), Floris, 2003.
- Lindenbaum, S.D.; Mathematical methods in physics, World Scientific, 1996
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