Why are complex functions rendered the way they are?

ztlawton shared this question 6 months ago
Answered

When I plot something like, for example, ℯ^(ί x), the function shows up as a circle with radius 1 as expected, but also includes additional circles of radius ℯ^n with n between -10 and 10, plus 21 rays emanating from the center and irregularly spaced around the circumference of the circle. More complicated functions show the same powers-of-ℯ and twenty-one-rays behavior. This happens in both the web and the desktop version. The only "Style" option available for complex functions is "Level of Detail", with no way to adjust even things like line thickness or the presence of these extra lines/curves. Why are complex functions rendered this way?

Comments (1)

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Hi! GeoGebra understands ℯ^(ί x) as function C->C rather than R->C and it renders it as a transform of the grid. You can see an explanation of this approach in 3Blue1Brown video

https://youtu.be/sD0NjbwqlYw?t=500

If you want to render a R->C function, you can use the Curve command


Curve(ℯ^(ί t),t,0,2pi)

For the missing line thickness setting: that sounds like a bug.

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