Quadratic Equation/Examples/x^2 + 1 = 0

$x^2 + 1 = 0$

has no root in the set of real numbers $\R$:

$x = \pm i$

where $i = \sqrt {-1}$ is the imaginary unit.

Proof

 $\ds x^2 + 1$ $=$ $\ds 0$ $\ds \leadsto \ \$ $\ds x$ $=$ $\ds \dfrac {-0 \pm \sqrt {0^2 - 4 \times 1 \times 1} } {2 \times 1}$ Quadratic Formula $\ds$ $=$ $\ds \pm \sqrt {-1}$ $\ds$ $=$ $\ds \pm i$ Definition of Imaginary Unit
$\blacksquare$