Question

Resolva, no campo dos números complexos, a equação x² - 6x + 13 = 0

Answer 1

Explicação passo-a-passo:

$x^2-6x+13=0$

$\Delta=(-6)^2-4\cdot1\cdot13$

$\Delta=36-52$

$\Delta=-16$

$\Delta=16\cdot(-1)$

$\Delta=16i^2$

$x=\dfrac{-(-6)\pm\sqrt{16i^2}}{2\cdot1}=\dfrac{6\pm4i}{2}$

$x'=\dfrac{6+4i}{2}~\longrightarrow~x'=3+2i$

$x"=\dfrac{6-4i}{2}~\longrightarrow~x"=3-2i$

$S=\{3-2i,3+2i\}$