An aside in another website reads:
Complex numbers were used to solve cubic polynomials, before complex numbers were invented.
I tried Googling this technique but didn't get anywhere.
What is this person talking about?
2026-03-29 02:28:40.1774751320
Solving cubics with complex numbers, before complex numbers.
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In the 16th century, Niccolo Tartaglia created a method for solving special cases of cubic equations, namely, those of the form $$x^3+ax^2=b$$ He later passed on the method to Gerolamo Cardano (who found out about them after a contest between Tartaglia and Antonio Fiore), on the condition that Cardano would never release the secret (which he eventually did, leading to an incredible public feud). Cardano found that, in certain cases, one must take the square of a negative number on order to use Tartaglia's method.
This appears to be what the quote is referring to.
It should be noted that the step involving a complex number was an intermediate one, and not of much importance to the final result. Additionally, Cardano eventually built off of the idea to solve cubics of the form $$x^3+ax^2+bx=c$$