Complex analysis in electrical circuits

[nhmllr]

When discussing the i (the imaginary unit) in a math class, my math teacher commented that that complex analysis is used in studying electrical circuits. I know a little about resistors and what not, but never have I seen complex analysis used this way. I've tried looking it up, but it's been fruitless. Has anybody else heard of this? What was he talking about?

Thanks.

 

[Meir Achuz]

Alternating current

 

[nhmllr]

Alternating current

Ah. http://openbookproject.net/electricCircuits/AC/AC_2.html

 

[Termotanque]

In general, complex impedance.

 

[technician]

This is a useful application in physics dealing with oscillations.
In analyzing complex numbers it is possible to show a relationship
e^iwt = Cos(wt) + iSin(wt)
This means that a physics expression such as V = VoCos(wt) can be written as the real part of a complex number Vo x e^iwt
Doing this means that you are dealing with exponential functions rather than Cosine and sine functions ...it is easier