[AstixAndBelix]

We didn't invent 'i' to "solve sqrt(-1)". This is an extremely common misconception about maths and how it progressed that unfortunately people get led into believing by lazy teachers every day

[rtpg]

So what did happen?

[aap_]

Square roots of negative numbers came up when solving cubic equations, even if the final solutions were all real. This meant the square root of a negative number was not something nonsensical the way you might claim for x^2 = -1, but actually...real in some sense.

[shagie]

There's a good YouTube video on it that includes an epic math battle.

Veritasium - How Imaginary Numbers Were Invented - https://youtu.be/cUzklzVXJwo

Solving the cubic was a physical thing back then. https://www.maa.org/press/periodicals/convergence/solving-th...