Particular Exponential Series

for any complex number x.

i) For complex number x.

ii) For complex number x,

iii) For example number x,

Corollary,

Working rules for solving problems

Rule 1:

Rule 2:

For any complex number, the series  is called the exponential series and is denoted by e^x.

Rule 3:

Rule 4:

Rule 5: