<s>
In	O
mathematics	O
,	O
the	O
n-dimensional	O
complex	B-Algorithm
coordinate	I-Algorithm
space	I-Algorithm
(	O
or	O
complex	O
n-space	O
)	O
is	O
the	O
set	O
of	O
all	O
ordered	O
n-tuples	O
of	O
complex	O
numbers	O
.	O
</s>
<s>
Complex	B-Algorithm
coordinate	I-Algorithm
space	I-Algorithm
is	O
a	O
vector	O
space	O
over	O
the	O
complex	O
numbers	O
,	O
with	O
componentwise	O
addition	O
and	O
scalar	O
multiplication	O
.	O
</s>
<s>
The	O
real	O
and	O
imaginary	O
parts	O
of	O
the	O
coordinates	O
set	O
up	O
a	O
bijection	B-Algorithm
of	O
with	O
the	O
2n-dimensional	O
real	O
coordinate	O
space	O
,	O
.	O
</s>
<s>
With	O
the	O
standard	O
Euclidean	O
topology	O
,	O
is	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
over	O
the	O
complex	O
numbers	O
.	O
</s>
<s>
Several	B-Architecture
complex	I-Architecture
variables	I-Architecture
is	O
the	O
study	O
of	O
such	O
holomorphic	O
functions	O
in	O
n	O
variables	O
.	O
</s>
