I think the best way to answer this question is by this fantastic video by Veritasium : [How Imaginary Numbers Were Invented](https://www.youtube.com/watch?v=cUzklzVXJwo&t=7s&pp=ygURaW1hZ2luYXJ5IG51bWJlcnM%3D)
It goes through the entire history and necessity for such a tool in Mathematics. Really fascinating
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