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Re:Walking Paths with Complex Numbers by pdkl95 on Friday December 02, 2016 @05:09PM (#13092771)
(first, I second ThrustVectoring's comment about algebraic closure. That's a key part of understanding complex numbers)

I recommend reading this[1] article. I found it very enlightening about why complex numbers are useful.

[1] https://acko.net/blog/how-to-fold-a-julia-fractal/

edit: Warning - [1] requires WebGL.

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