complex exponential signals

[bhuvaneshnick]

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

 

[Tony Stewart]

frequency response formula is complex sine
time response formula is exponential

 

[bhuvaneshnick]

i dont get you

 

[Tony Stewart]

What graph? Show what you are given

 

[bhuvaneshnick]

my question is more general sir
take for example sin(t)(amplitude of 1) and jsin(t)(amplitude of j). Do both signal just vary only by amplitude or anything more than that.

 

[Tony Stewart]

Complex sine are treated as Vectors with Real on X axis and Imaginary ( j) on Y axis.
Imaginary axis is used for Reactive components like L ( inductance ) and C (capacitance) since ideally they do no dissipate real energy , but can store energy and resonate with a sine when there are L & C

 

[Tony Stewart]

https://en.wikipedia.org/wiki/Euler's_formula

the relationship of sin and cos waves from real and reactive components results in a phase and amplitude change

example
the resulting vector is the phase angle relation between voltage and current in resistive and reaction components in a network with the same frequency.

the derivative of a sin is the cosine or 90 deg vector shift.

 

[bhuvaneshnick]

i am sailing in boat moving 3 units in north moving 4 units in east having 3+4j as vector now i want to rotate it to 90 degree counter clockwise so i just multiply by i.Then i get the answer ,but i want to know it can be done in harder way,i mean how to do same rotation with using complex plane .THank you in advance