Question

Resolva, no campo dos números complexos, a equação: x^2-2x+6=0 Calculo por favor, obrigada

Answer 1

$x^2 - 2x + 6 = 0\\\\x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4.6.1}}{2.1}\\x = \frac{2 \pm \sqrt{4 - 24}}{2}\\x = \frac{2 \pm \sqrt{-20}}{2}\\x = \frac{2 \pm 2i.\sqrt{5}}{2}\\\\x_1 = \frac{2 + 2i.\sqrt{5}}{2} = 1 + i.\sqrt{5}\\x_2 = \frac{2 - 2i.\sqrt{5}}{2} = 1 - i.\sqrt{5}$