# Complex number space

I call the meeting that the whole prioritized n-tuple consisting of the complex number makes the double bare n-dimension (number) space (すうくうかん British: complex n-space) in the mathematics and write it with Cn. If it is n-重 Tsumoru Descartes of meeting C which the whole complex number makes and writes this in a sign

${\displaystyle \mathbb {C} ^{n}= (z_{1},\ldots ,z_{n})\mid z_{i}\in \mathbb {C} =\underbrace {\mathbb {C} \times \mathbb {C} \times \dotsb \times \mathbb {C}} _{n}}$

である. Each variable zi of the number of double bare n-dimensions space is called a coordinate or a coordinate ingredient (double bare). I call it the n-dimension double bare coordinates space (n-dimensional complex coordinate space) in a meaning called the space that the whole n-dimension double bare coordinates makes.

## Structure on the number space

In the number of double bare ­ space, the sum and the scalar every ingredient become the vector space in the complex number health by doubling it (they can make bijection between double bare n-dimension space Cn and true 2n-dimension space R2n if they think about the real part of each coordinate ingredient and an imaginary part). Furthermore, I put normal phase (standard ), and Cn makes phase linear space in the complex number health.

## Function on the number space

When a function defined on an open set of the double bare n-dimension space is Masanori, I say when it becomes the Masanori function about each coordinate variable each. The many variables double bare functions theory is a study of the Masanori function of the n-variable. Generally the double bare n-dimension coordinate space is 接空間 for the Masanori coordinate system in double bare manifolds.

## References

• Gunning, Robert; Rossi, Hugo, Analytic functions of several complex variables