Question

What is the solution of the equation when solved over the complex numbers? X2+24=0

Answer 1

You can rearrange the equation as follows:

$x^2 = -24$

Using real numbers, it would be impossible for a square to be negative, but using imaginary numbers it is possible, since $i^2 = -1$

So, since $\sqrt{24}^2 = 24$, we know that

$(i\sqrt{24})^2 = i^2\cdot \sqrt{24}^2 = (-1)\cdot 24 = -24$

So, the solutions to the equations are

$x^2 = -24 \iff x = \pm\sqrt{-24} = \pm i \sqrt{24}$