Complex analysis in electrical circuits

AI Thread Summary
Complex analysis is essential in studying electrical circuits, particularly in the context of alternating current (AC) and complex impedance. The relationship between complex numbers and oscillations is highlighted by the equation e^iwt = Cos(wt) + iSin(wt), which allows for the representation of AC voltage as a complex number. This approach simplifies calculations by using exponential functions instead of trigonometric functions. Understanding this concept can enhance the analysis of circuit behavior and improve problem-solving efficiency. Overall, complex analysis provides a powerful tool for electrical engineers and physicists.
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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.
 
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Alternating current
 
clem said:
Alternating current

Ah. http://openbookproject.net/electricCircuits/AC/AC_2.html
 
In general, complex impedance.
 
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
 
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