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

**URL:** <https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645>\
**Category:** Factual Questions\
**Created:** [February 8, 2020, 10:11pm UTC](https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645 "2020-02-08T22:11:41Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\
**Post date:** [February 8, 2020, 10:11pm UTC](https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645/1 "2020-02-08T22:11:41Z")

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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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**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\
**Post date:** [February 8, 2020, 10:14pm UTC](https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645/2 "2020-02-08T22:14:34Z")

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Feynman may be able to help  
[https://www.feynmanlectures.caltech.edu/I\_22.html](https://www.feynmanlectures.caltech.edu/I_22.html)

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**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\
**Post date:** [February 13, 2020, 6:50am UTC](https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645/3 "2020-02-13T06:50:59Z")

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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.

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**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\
**Post date:** [February 13, 2020, 7:36am UTC](https://boards.straightdope.com/t/visualizing-or-otherwise-comprehending-aside-from-formulas-raising-values-to-complex-powers/847645/4 "2020-02-13T07:36:07Z")

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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.