In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted C n {displaystyle mathbb {C} ^{n}} , and is the n-fold Cartesian product of the complex plane C {displaystyle mathbb {C} } with itself. Symbolically, In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted C n {displaystyle mathbb {C} ^{n}} , and is the n-fold Cartesian product of the complex plane C {displaystyle mathbb {C} } with itself. Symbolically,