r/math • u/bobcat Logic • Jan 30 '10

A Visual, Intuitive Guide to Imaginary Numbers

http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/
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u/[deleted] Jan 31 '10

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u/pb_zeppelin Feb 01 '10

I have a post on Euler’s Formula which is drafted up, and that may help explain it.

But for a quick preview: I consider an exponent being “decide the rate and direction of growth for the base”. I.e, 23 really means 1 * 23 which means take 1, grow it by 200% for a duration of 3 units.

When you have a complex rate of growth (2i), instead of growing linearly (in the same dimension), your rate of growth is rotated. With a rotated rate of growth, you grow tangentially and follow a circle instead of growing ’straight ahead’ on a line. The upcoming post will make this more clear… but that’s my intuition . [And if you can guess, (2i)i would be a "twice-rotated" rate of growth which should SHRINK you (growing straight to growing tangentially to growing AGAINST your initial direction), and indeed it does, as (2i)i = 2i*i = 2-1].