Euler's formula

[chopficaro2]

how is euler's formula useful? it must have something to do with converting from the time domain to the phasor domain and back, but i can do that without euler's formula

 

[Skogsgurra]

Good for you!

Euler's formula is a beauty. It describes the relation between e with an imaginary exponent, Pi and the fundamental quantities zero and unity. It also helps in deriving many trigonometric formulas.

But you would probably not see the beauty in it. Do your conversions the way you are used to.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[sibeen]

It must be fun reading a lot of EE papers that use the exponential form, instead of polar or rectangular, for vectors without at least a rudimentary knowledge of Euler's formula.

Very interesting reading indeed.

 

[electricpete]

As mentioned, you can derive trig formulas:
expI(A+B) = exp(IA) exp(IB) = (cosA+IsinA)(cosB+IsinB)
expI(A+B) = cosA*cosB-sinAs(inB + I(cosA*sinB + cosB*sinA)
cos(A+B) = Re { expI(A+B)} = cosA*cosB-sinA*sinB
sin(A+B) = Im { expI(A+B)} = cosA*sinB + cosB*sinA[b]
Note there was no memorization required, just simple laws of exponents. And in many problems you can replace cumbersome trig calculations with simpler more streamlined complex exponential trig calculations.

The complex form of Fourier series is much more compact than the real form and transitions neatly to the Fourier transform.

Whether it is "useful" depends on what you're doing. You won't get far into a signals and systems textbook without Euler's relation. It also shows up in differential equations. There is also a whole field of complex analysis which yields tools such as conformal transformation to determine electric/magnetic field solutions.

But for single-frequency sinusoidal steady state power systems analysis, I don't think it matters whether you represent a phasor as a complex exponential or a magnitude/angle phasor with some predefined rules of what you can do with such phasors (those rules happen to match the rules of complex exponentials). That would be a matter of preference.

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