5.1 The Complex Exponential Function
Recall that the real exponential function can be represented by the power series . Thus it is only natural to define the complex exponential , also written as , in the following way:
Definition 5.1 (Exponential Function). The definition of exp(z) is
Demonstration for Definition 5.1.
We can use Mathematica to sum a power series.
The ratio test can be used to show that the infinite series converges for all values of z.
(c) 2006 John H. Mathews, Russell W. Howell