Question

Resolva, no conjunto dos números complexos, a equação x² + 2x + 5 = 0.

Answer 1

Lembrando que i² = -1, temos que:

$x^2+2x+5 = 0\\\\\Delta = b^2-4ac = 4-4*1*5 = 4-20 = -16\\\\x = \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{-2\pm \sqrt{-16} }{2}\\\\\ \sqrt{-16} = \sqrt{16i^2} = 4i\\\\x' = \frac{-2+4i}{2} = \frac{2(-1+2i)}{2} = -1+2i\\\\x'' = \frac{-2-4i}{2} = \frac{2(-1-2i)}{2} = -1-2i \\\\\boxed{S = \{-1-2i,-1+2i \}}$

Espero ter ajudado. :))

Answer 2

$x^2+2x+5=0$

$\Delta=2^2-4\cdot1\cdot5=4-20=-16=16i^2$

$x=\dfrac{-2\pm\sqrt{16i^2}}{2\cdot1}=\dfrac{-2\pm4i}{2}=-1\pm2i$

$x'=-1+2i$   

$x"=-1-2i$