https://betterexplained.com/articles/understanding-why-complex-multiplication-works/ Math lessons that click Thu, 13 Aug 2026 14:20:11 +0000 hourly 1 https://betterexplained.com/articles/understanding-why-complex-multiplication-works/#comment-568429 Thu, 13 Aug 2026 14:20:11 +0000 http://betterexplained.com/?p=1289#comment-568429 The REAL secret in complex is that multiplication is ROTATION. Chew on that alone, philosophically. Make some sense out of that.

]]> https://betterexplained.com/articles/understanding-why-complex-multiplication-works/#comment-568302 Sat, 02 Sep 2023 15:01:27 +0000 http://betterexplained.com/?p=1289#comment-568302 “When you have satisfied yourself that the theorem is true, you start proving it." I didn't understand that quote (plus, english is not my mother tongue).

]]> https://betterexplained.com/articles/understanding-why-complex-multiplication-works/#comment-568037 Sun, 10 Jan 2021 23:25:15 +0000 http://betterexplained.com/?p=1289#comment-568037 Great work! Fantastic intuition. Haven't finished it yet, but it might be nice to talk about the negative slope perpendicular theorem, and the intuition for that theorem. Take a complex number like a+bi. It's a vector (a,b), like a line with slope b/a. But what does multiplying by i do? It turns imaginary to real, but negative real, and real to imaginary, so the new vector has slope -b/a! It makes a vector its perpendicular; i has this multiplicative property, making it so useful!

]]> https://betterexplained.com/articles/understanding-why-complex-multiplication-works/#comment-567615 Wed, 04 Sep 2019 21:45:37 +0000 http://betterexplained.com/?p=1289#comment-567615 Thank you! This really helped me!

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