Imaginary numbers were invented too early, that is why the usual explanations following the historical development are so mysterious. The notion of Sqrt(-1) doe

Imaginary numbers were invented too early, that is why the usual explanations following the historical development are so mysterious. The notion of Sqrt(-1) does not help to explain what they actually are. In fact imaginary "numbers" are not numbers. They cannot be ordered by size. Imaginary "numbers" are also not vectors in the geometrical sense. This is because you can multiply two geometrical vectors and get a scalar as result (scalar product). But if you multiply two imaginary "numbers" you get another imaginary "number", so this is different to a geometrical vector. In fact imaginary "numbers" are transformations or operators, because they multiply like operators/matrices and they act on geometrical vectors like rotation matrices. Group theory makes all that very clear: Imaginary "numbers" are just the elements of the group SO(2), the group of rotation operations in 2D (multiplied with a scaling factor). However the invention of group theory started only with Galois in 1832 when trying to solve not the cubic, but the quintic. And the powerful notation of matrices as is ubiquitous nowadays was only invented in 1913 (by Cuthbert Edmund Cullis, see https://en.wikipedia.org/wiki/Matrix_(mathematics)#History https://en.wikipedia.org/wiki/Matrix_(mathematics)#History) Unfortunately mathematicians (and YouTubers) don't stop to teach the confusing outdated notions of imaginary/complex numbers rooted in the 18th and 19th century. And unfortunately this video belongs to the many videos just repeating the same old stuff over and over again.