Question

what causes the need for imaginary numbers?

Answer 1

idk, I guess to be able to put something containing a square root (or 4th, 6th and even root) into a better form.

Answer 2

Well one example of why we need them, is because we want polynomials to always factor. In the real numbers, the polynomial \(x^2+1\) doesn't factor. There are no real roots of this polynomial. But the complex numbers are special in that no matter what polynomial you have, it will always factor in the complex numbers.

Answer 3

that too :)

Answer 4

I should note that it's rather difficult to prove that the complex numbers have this property, but it is true.

Answer 5

you get the idea @veronicafresta, right? to be able to factor polynomials (such as a^2+b^2) and to be able to write the square root in a better form....