DiscoverWell-defined & WonderfulComplex Exponentials, trigonometric functions Part 3 - Euler's formula
Complex Exponentials, trigonometric functions Part 3 - Euler's formula

Complex Exponentials, trigonometric functions Part 3 - Euler's formula

Update: 2023-02-20
Share

Description

This episode is concerned with one of the most striking formulas in mathematics. Namely the relationship between sin, cos, and the complex exponential for purely imaginary arguments. To derive this formula, we require a closer look into the complex exponential function. The most important fact that we will derive is that no matter the modulus of the purely imaginary number put into the complex exponential the result will always be on the unit circle. Whether or not we reach all elements of the unit circle in the complex plane while running through all purely imaginary numbers remains to be seen in the next episode.


Picture taken from https://hyrodium.tumblr.com/post/106601751454/euler1

Comments 
In Channel
loading
00:00
00:00
x

0.5x

0.8x

1.0x

1.25x

1.5x

2.0x

3.0x

Sleep Timer

Off

End of Episode

5 Minutes

10 Minutes

15 Minutes

30 Minutes

45 Minutes

60 Minutes

120 Minutes

Complex Exponentials, trigonometric functions Part 3 - Euler's formula

Complex Exponentials, trigonometric functions Part 3 - Euler's formula

profmoppi