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#1
02-08-2020, 05:11 PM
 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?
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#2
02-08-2020, 05:14 PM
 Member Join Date: Oct 2000 Posts: 7,141
Feynman may be able to help
https://www.feynmanlectures.caltech.edu/I_22.html
#3
02-13-2020, 01:50 AM
 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
02-13-2020, 02:36 AM
 Guest Join Date: Nov 2009 Posts: 5,787
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.

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