How can one visualize the multiplication/division of a complex number, z, by a real number, an imaginary number, or another complex number?
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4Does this very similar question help you? – Noble Mushtak Jun 26 '16 at 21:55
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Yes, it does; however, I have not taken a pre-calculus course so the mathematics behind the answers are still unfamiliar to me. – user348382 Jun 26 '16 at 22:06
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@guest Possibly. But the answers are completely clear (add angles, multiply lengths for multiplication). So having grasped that you should be able to figure out the rest for yourself. The reference to Visual Complex Analysis is also worth following up. – almagest Jun 27 '16 at 05:25
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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.
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