Exponential Functions Part 3: Complex Numbers

In the final installment of our three-part series on exponential functions, we explore its application to complex numbers. This leads us to Euler's formula, which unites complex numbers, exponential functions, and trigonometry.

0:17 An introduction to complex numbers
1:20 Plotting the complex values of the exponential function
2:29 Euler's Formula
3:05 Proof of Euler's Formula using Taylor series
3:41 Interesting exponential results of complex numbers

Synthesizer modules used:
* Sputnik Dual Oscillator
* Metasonix RK5 Dual Low Pass Gate
* Qu-Bit Prism
* Strymon Magneto
* After Later Pique

Software synthesizers:
* Arturia CMI V
* Arturia CS80 V
* Kontakt w/ Son of Grindhouse library

Cartoon background music:
* Arturia Stage 73 V
* Arturia Mellotron V
* EastWest Fab Four

Equations created w/ LaTeX
Graphs created with gnuplot

[SerenaToxicat]

This is great, very informative and well done!

[nutritionalyeast]

i love this video, i knew this stuff before but i never seen the 3d graph of exponential function in the complex plane, it makes it much easier to understand

[julianguffogg]

Takes me back to when I did math at 17...

[willhelmke]

So, I'm just wondering because I am trying to figure it out, how this applies to electrical signals and exponential converters in say a VCO design? I've been struggling in general to understand these relationships wonlytrash maker cat eye emoji😺