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complex corkscrew

created by Oneiromancer

(thing) by Oneiromancer (2.1 wk) (print)   ?   (I like it!) Tue Jun 26 2001 at 4:40:21

The visual appearance of the graph of the function e^(ix). If x describes the distance along the corkscrew, the output will wrap around and around, much like a corkscrew. If you want to reverse the chirality of the corkscrew, all you have to do is flip one of the dimensions (as you always do to flip chirality), such as by taking the function e^(-ix).

If one projects either of these onto the reals, the result is cos(x) == cos(-x). If one projects either of them onto the imaginaries, one will get sin(x) or sin(-x) == -sin(x) depending on the sign you used. This function and its relatives are widely used in physics and electronics.


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