Gauss deciphered complex numbers over 200 years ago, yet they still remain mysterious for most. Two geometric meanings are explained: points of the plane and transformations of the plane.
“For any equation one can imagine as many roots [as its degree would suggest], but in many cases no quantity exists which corresponds to what one imagines.”
Euler 1777
Introduced the notation 𝑖 and called it impossible.
Wessel 1797
Argand 1806
Gauss 1831
“If this subject has hitherto been considered from the wrong viewpoint and thus enveloped in mystery and surrounded by darkness, it is largely an unsuitable terminology which should be blamed. Had +1, -1 and √ −1, instead of being called positive, negative and imaginary (or worse still, impossible) unity, been given the names say, of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity.”
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Two amazing math jokes
Why Romans sucked in algebra?
Because X was always ten.
Why Mayans counted in the base-20 numeric system?
Because they did not wear shoes.
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Sources
Complex analysis: A Visual and Interactive Introduction by Juan Carlos Ponce Campuzano, licenced under CC BY-NC-SA 4.0, available at https://complex-analysis.com/
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