function with complex numbers

Niek Sprakel shared this question 2 years ago
Answered

Hi.

Is there any way to work with functions involving complex numbers in GeoGebra?

For instance, there is a paper containing some conformal mappings from the unit disk to period 3 bulbs of the mandelbrot.

https://i.imgur.com/l3OeKgN.png


https://tinyurl.com/y7jmuc2f


I can use the first equation by using that function to map points along the unit circle on (part of) the border of the period three bulb. But the 2nd and 3rd equation involve the imaginary unit i. Is there any way to work around this in GeoGebra?


https://i.imgur.com/dSo1e1c.png

Best Answer
photo

In another paper there were more convenient equations and this allowed me to obtain the desired results in GeoGebra.

http://www.ams.org/journals...

https://i.imgur.com/19Md0L5.png

Comments (4)

photo
1

Please post your .ggb file (and the equations!)

photo
1

Ok, I've added the ggb file.

It turns out that the equations are a bit buggy. So far I've only managed to debug the first of the three equations (so one minus sign in that equation has been changed to a plus sign).

I've got a clunky way to work my way around the complex number i in the 2nd and 3rd equation by splitting them up in three parts and using two complex numbers to work them back in. This seems to work, but I've had no luck debugging those equations yet.

So as the variable a runs from 0 to 2 pi, the complex number A traces around the unit circle and f_3, which represents the first equation, maps it to sections of the period 3 bulbs (A_3 traces this mapping).

f_3a, f_3b and f_3c in combination with c_1 and c_2 are supposed to do the same for the second and third equation, but those equations seem flawed so it's a bit of a puzzle to fix them so they work likewise in GeoGebra.

photo
1

In another paper there were more convenient equations and this allowed me to obtain the desired results in GeoGebra.

http://www.ams.org/journals...

https://i.imgur.com/19Md0L5.png

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