Reply
 
Thread Tools Display Modes
  #1  
Old 02-08-2020, 05:11 PM
Frylock is offline
Guest
 
Join Date: Jun 2001
Posts: 19,739

Visualizing (or otherwise comprehending aside from formulas) raising values to complex powers


I can do the math, I know about Euler's formula, etc etc. But I am wondering if there is anything written that can help the reader intuitively grasp what kind of transformation "raising to a complex power" represents. Google turns up articles that just focus on how to do the math with symbols. I'm hoping to also know of a more intuitive way to talk about it.

Any ideas?
__________________
hopelessgeneralist.blogspot.com
  #2  
Old 02-08-2020, 05:14 PM
Andy L is offline
Member
 
Join Date: Oct 2000
Posts: 7,141
Feynman may be able to help
https://www.feynmanlectures.caltech.edu/I_22.html
  #3  
Old 02-13-2020, 01:50 AM
rowrrbazzle's Avatar
rowrrbazzle is offline
Guest
 
Join Date: Jul 1999
Location: Chicago
Posts: 8,769
For a visualization, you might find one on YouTube. Channels to try are 3blue1brown and mathologer. When you bring up one of their videos, also check the related videos that come up.
  #4  
Old 02-13-2020, 02:36 AM
Melbourne is online now
Guest
 
Join Date: Nov 2009
Posts: 5,786
For those of us who are fortunate enough to work in one dimension, "raising to a complex power" is the same as "rotating through the imaginary dimension". The real part of the complex gives you a magnitude, the imaginary part gives you an angle of rotation. You can picture the value advancing along a screw thread (with a zero internal radius) as the "power" is increased.
Reply

Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 01:49 AM.

Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2020, vBulletin Solutions, Inc.

Send questions for Cecil Adams to: cecil@straightdope.com

Send comments about this website to: webmaster@straightdope.com

Terms of Use / Privacy Policy

Advertise on the Straight Dope!
(Your direct line to thousands of the smartest, hippest people on the planet, plus a few total dipsticks.)

Copyright 2019 STM Reader, LLC.

 
Copyright © 2017