The complex Exponential Function is the complex function that we can define as a power series and that extends the real Exponential function to complex values

This series converges everywhere in the complex plane.

If we increase the degree of the Taylor polynomial, this polynomial approaches the function more and more. We can see it if we look at the Remainder (the difference between the function and the polynomial):

The Exponential Function is periodic with period .

LINKS

	The Complex Exponential Function The Complex Exponential Function extends the Real Exponential Function to the complex plane.
	Taylor polynomials: Exponential function By increasing the degree, Taylor polynomial approximates the exponential function more and more.
	The exponential as the inverse of the logarithm (Spanish)
	Taylor polynomials: Complex Cosine Function The power series of the Cosine Function converges everywhere in the complex plane.
	Taylor polynomials: Rational function with two complex singularities We will see how Taylor polynomials approximate the function inside its circle of convergence.
	More about complex functions Examples of complex functions: polynomials, rationals and Moebius Transformations.