This is my entry into the Second Summer of Math Exposition. I used to wonder about these questions ever since my first year in university, so in a sense this is a rather personal subject for me. I hope that this video reaches someone else who is also wondering about these issues.
Here's the Desmos document for visualizing the n complex roots of any complex number:
www.desmos.com/calculator/1v4...
Videos mentioned in order of apparition:
e to the pi i, a nontraditional take (old version)
• e to the pi i, a nontr...
The 'Everything' Formula - Numberphile
• The 'Everything' Formu...
Winding numbers and domain coloring
• Winding numbers and do...
The 5 ways to visualize complex functions | Essence of complex analysis #3
• The 5 ways to visualiz...
Visualizing Complex-Valued Functions
• Visualizing Complex-Va...
Jeff Tupper's webpage on the graph of x^x
www.peda.com/grafeq/gallery/ro...
A relevant Stack Exchange question and answer that touches on these ideas:
mathematica.stackexchange.com...
Chapters:
00:00 Intro and problem motivation
01:49 The R-to-C graph of x^a
04:37 The R-to-C graph of a^x
06:37 Rotations in complex exponentiation
07:27 The R-to-C graph of x^x
08:17 An alternative version of the graph of x^x
12:37 Recap of the various graphs of x^x
13:49 Homework
14:09 Summary and outro
Music by Vincent Rubinetti
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
Негізгі бет Ойындар What is the graph of x^a when a is not an integer? An unusual look at familiar functions
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