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The present work has been analysed graphically the approximations as Taylor series of functions of a complex variable, using the domain coloring. In this method each point is coloring according to the value of range. Functions of a complex variable have a property to associate one point of the plane other point of the plane, what describe them as vectorial functions from the complex plane to the complex plane. A complex function is called a holomorphic function in a region if is differentiable in all points of that region. Holomorphic functions can be described as power series.

Qualitative analysis of approximations of functions of a complex variable by Taylor series