How can one visualize the multiplication/division of a complex number, z, by a real number, an imaginary number, or another complex number?
2026-03-28 01:06:38.1774659998
What is a geometric interpretation of multiplication/division in the complex plane?
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By rotation and stretching. Multiplication by $z=re^{i\theta}$ with $r$ and $\theta$ real corresponds to rotating the plane over $\theta$ radians, and stretching the plane in all directions by a factor $r$.
I also find that this video has very nice animations illustrating the geometry of arithmetic on complex numbers.