The historical origin of the imaginary unit i is tied to Gerolamo Cardano and the solution of the cubic equation.

The cubic equation is ax^3+bx^2+cx+d=0 and the specific case that brought about the invention of the imaginary unit was the situation when the discriminant of this equation D=18abcd-4ac^3-27a^2d^2+b^2c^2-4b^3d is greater than 0. This case is called *casus irreducibilis* or 'the irreducible case'. Cardano had found the solution to the cubic equation, the famous *Cardano's solution*, but in the *casus irreducibilis* his solution would only work if the result of a square root could be a negative number. This led him to invent the imaginary unit.

Much later on, in 1730 it was discovered by Abraham de Moivre that the use of the imaginary unit can make certain trigonometric calculations much more compact. This was further studied by Leonhard Euler, leading into the creation of a branch of mathematics called *complex analysis*, where the imaginary unit plays a key part.

This has been a brief overview of the history of the imaginary unit. Would you like to hear more of any of the things I mentioned?
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