Complex Number Tutorial

This type of thing just adds to the confusion about the use of complex numbers in the analysis of linear systems. The concept of the phasor (phase-vector) is at the core of their utility, and this derives from the invertible morphism between the analytical operations of differentiation and integration on real functions and the the algebraic operation of multiplication by jw and 1/jw on their complex representations.

I think the last two of these programs are not loading correctly in some computers. My home computers load fine , but I am seeing other probs. If the last two programs don't load, I am sorry. I am trying to figure out why.

On the last two programs, click to download and then close out the program, then reclick , and it comes up correctly. Don't know why , yet

I find that you are the confused one. The properties of the Euler identity are what brings up the vector representation. The conversions between differentiation and multiplication are related to conversion between time domain and frequency domain.

JosephKK

domain and frequency domain.

I would say that you have it backwards. It was the algebraic properties of the *phasor* that enabled calculations of solutions to real problems in systems of differential equations that made the whole Fourier/LaPlace thing go and not vice versa. Euler's identity very nicely tied into the best known basis functions of the time. Typical engineer...

s.

Pretentious jibberish

s.

Use of the Laplace transform can give the complete time domain response. Phasors don't do that. Phasors only give the forced response (steady state ac analysis).