A complex space is a mathematical space based upon complex numbers. Types of complex space include:
Complex affine space, an affine space over the complex numbers, with no distinguishable point of origin Complex analytic space, a generalization of a complex manifold, with singularities allowed Complex coordinate space, the set of all ordered n-tuples of complex numbers Complex Hilbert space, a complex inner product space that is also a complete metric space Complex manifold, in differential geometry, a manifold with an atlas of charts to the open unit disk such that the transition maps are holomorphic Complex projective space, a projective space with respect to the field of complex numbers Unitary space, a vector space with the addition of an inner-product structure Complex vector space, a vector space whose scalar field is the complex numbers