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On the complex plane, curves given by an equation of the form: $$ |z-z_1|\cdot |z-z_2| \cdots |z-z_n| = C $$ with $ C \gt 0$, are known as general lemniscates, or Cassinian curves with $n$ foci.

I find it's difficult to depict their shapes on the complex plane. Can you tell me their general shapes, or where can I find them?

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http://www.mathcurve.com/courbes2d/cassinienne/cassinienne.shtml (in French, but the figures are easy to find...)

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  • $\begingroup$ This is a nice link, but at least a short (English?) summary of what's in the link would be more helpful. $\endgroup$ – J. M. is a poor mathematician Jul 7 '16 at 8:00
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If you are interested in a deep study of such curves have a look here:

http://www.mathe8.uni-bayreuth.de/Personen/CatPers/PubliCat/POlLemn-CatPal-Topology.pdf

you should also have a look to there referens therein.

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