# complex exponential signals

Discussion in 'Electronics Homework Help' started by bhuvanesh, Mar 2, 2015.

1. ### bhuvanesh

201
0
Aug 29, 2013
what makes complex exponential special.its just an addition of cosine and sine with imaginary amplitude ,isn't it?.In my book the waveform for real exponential is given and for complex exponential signal the graph given is just sinusoidal signal .so i cannot differentiate complex exponential and sinusoidal signal.Thank you in advance

2. ### Merlin3189

250
69
Aug 4, 2011
Quite so! This is Euler's Relation.

A complex exponential can be written in terms of sin and cos.
And sin and cos can be written in terms of complex exponentials.

e^ix = cos(x) + i sin(x)

sin(x) = {e^ix - e^-ix} / 2i
cos(x) = {e^ix + e^-ix} / 2

The complex exponential form is used when it is more mathematically convenient.

3. ### bhuvanesh

201
0
Aug 29, 2013
my professor stressed the line"complex exponential play big role in signals and system and it makes the things easier".i need strong reason to agree that.Thank you in advance  