awesome !!! finally I understood complex numbers !!! thank you !

12:00 even though I am teaching my students how to calculate filters with complex number, I have not thought of using the complex logarithm here. Instead I would have used the argument of the resulting complex number, which is the angle towards the real axis. In cmath this would be the function cmath.phase() and the result would be in radians which has to be scaled accordingly. return cmath.phase(result)/cmath.pi*180 But I must admit that using cmath.log() as the inverse function of e ** (1j * phi) is interesting.

at 45:57 couldn't you just use the two points on the circle and calculate the magnitude of a vector between those two points? (I2 - I1)^2 + (Q2-Q1)^2 or something in that direction? And isn't that just vector subtraction?

These videos belong to this guy twitter.com/michelleossmann?lang=en. This channel has just uploaded them.

these videos do not belong to you.

Please stop putting arrows in the negative direction on coordinate systems (both 1d and 2d). It's... bothersome to me. at 34:00 you explain that you want to plot your samples in the complex plane. However to place a point in that plane you need a few samples to begin with. You couldn't know from a single sample whether it's the peak of the waveform of on the rising edge or falling edge or how high it's going to be. You need more information. You just shifted the "how do we calculate the envelope" problem to "how do we draw this in 2d to represent the envelope". Really I don't understand where you pull the complex part of the real signal from. You get a waveform and suddenly you invent an extra dimension and pull the values for that seemingly out of your rear end and then propose a super simple algorithm to do the maths. Complex numbers are well and good and all, but the problem of finding an algorithm is not the real problem here. How do you get from one coordinate system to the other? Do you just take the x value and use it as a factor of i and add that to the real value of the signal? Then you'd need to keep track of time, and find a corrective factor to sync up your carrier frequency with your i so that one cycle in the carrier wave corresponds to 2xi.