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Complex
Analysis. FreeTutorial
A complex exponential function
 or
exp(z) can be represented
by the power series:
The complex exponential
function gives
the same values as the corresponding exponential
function for real variables when the number
z
is a real number.
The exponential function
is a solution to the differential equation
with the initial condition
The complex exponential
function is
a periodic function; 
is a period of the function.
To show it let us use Euler’s
identity:
Let
x =
- iz, then
Let z
= z
+
=
So
and is
a period of the complex exponential function.
by
Tetyana Butler
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