("True") complex curves-Part 2: polar coordinates examples

Complex valued functions w=f(z) represent 2D manifolds, ie surfaces, in 4D space defined by (x,y,u,v), where z=x+iy and w=u+iv. These surfaces can be described by 3D parametric curve families, which in turn can be rendered in 3D space, where they also generate a "curve surface".
Besides parametric curves in cartesian coordinates (x=cst and y=cst) discussed in the previous video, here you'll find a description of parameter curves in polar coordinates : z=Z e^(iζ) and w=W e^(iω).
website:
www.wugi.be/qbComplex.html
playlist:
• wugi's Visualization o...
channel:
/ @wugionyoutube
Desmos 3D example:
www.desmos.com/3d/yauxpxnkpl

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why is the music off of a horror movie 😭

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all is relative. Eurovision is pure horror to me :o)