Consider the real-valued exponential function defined by . It has the following properties:

1)

2)

3)

We want to extend the exponential function to the complex numbers in such a way that

1)

2)

3)

But has been already defined for and we have .

Last modified on 18 October 2010, at 15:57
# Complex Analysis/Elementary Functions/Exponential Functions

Consider the real-valued exponential function defined by . It has the following properties:

1)

2)

3)

We want to extend the exponential function to the complex numbers in such a way that

1)

2)

3)

But has been already defined for and we have .