Adjective
complex-differentiable (not comparable)
(mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.
In other words, if u and v are real-differentiable functions of two real variables, obviously u + iv is a (complex-valued) real-differentiable function, but u + iv is complex-differentiable if and only if the Cauchy–Riemann equations hold. Source: Internet
Definition The function is not complex-differentiable at zero, because as shown above, the value of varies depending on the direction from which zero is approached. Source: Internet
This means that, in complex analysis, a function that is complex-differentiable in a whole domain (holomorphic) is the same as an analytic function. Source: Internet