Euler's formula
Euler's formula
(OP)
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
When was the last time you drove down the highway without seeing a commercial truck hauling goods?
Download nowINTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS Come Join Us!Are you an
Engineering professional? Join Eng-Tips Forums!
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail. Posting GuidelinesJobs |
|
RE: Euler's formula
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
www.gke.org
--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...
RE: Euler's formula
Very interesting reading indeed.
RE: Euler's formula
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
[b]sin(A+B) = Im { expI(A+B)} = cosA*sinB + cosB*sinA[[b]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.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.