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A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

Complex Analysis

Let z=x+iy and f(z)=u(x,y)+iv(x,y) on some region G containing the point z_0. If f(z) satisfies the Cauchy-Riemann equations and has continuous first partial derivatives in ...

A complex manifold is a manifold M whose coordinate charts are open subsets of C^n and the transition functions between charts are holomorphic functions. Naturally, a complex ...

A variable that may assume complex values.

A complex polynomial is a polynomial with complex coefficients.

A complex number may be taken to the power of another complex number. In particular, complex exponentiation satisfies (a+bi)^(c+di)=(a^2+b^2)^((c+id)/2)e^(i(c+id)arg(a+ib)), ...