Making peace with complex numbers [English]
#imaginarynumber #complexnumbers #eular
This video is about my journey in lockdown towards making peace with imaginary numbers and intuitive proof of Euler's formula. I discussed intuitions behind why it makes sense to consider imaginary numbers as a separate axis, what it means to have an imaginary exponent and why complex exponential function relates to cosine and sine functions.
Slides and matlab/octave code for plots: https://tinyurl.com/cmplxnos
Some useful links I mentioned in talk
Real Imaginative Guide to Complex Numbers:
https://wirelesspi.com/a-real-imagina...
A Quadrature Signals Tutorial:
https://www.dsprelated.com/showarticl...
Welch Labs - Imaginary numbers are real:
• Imaginary Numbers Are Real [Part 1: Introd...
3Blue1Brown - Taylor Series:
• Taylor series | Chapter 11, Essence of cal...
How imaginary numbers were invented:
• How Imaginary Numbers Were Invented
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CONTENT
(0:00) Background: Complex numbers, Addition, Multiplication
(5:50) Why iota i.e. sqrt(-1) makes sense as 90 degree rotation
(8:14) Intuitive proof of Euler's formula
(18:35) Bonus - Further intuition behind the proof