Question

Resolva no Universo de números complexos as equações Por favor .

Answer 1

a )

$x^2+25=0\\x^2=-25\\x=\pm \sqrt{-25} \\x=\pm5i$

b )

$x^2+121=0\\x^2=-121\\x= \sqrt{-121} \\x=\pm11i$

c )

$x^2-6x+13=0\\ \\\Delta=b^2-4ac\\\Delta=36-4.1.13\\\Delta=-16\\\ \\x= \frac{-b\pm \sqrt{\Delta} }{2a}$

$x= \frac{6\pm4i}{2} \\ \\x= \frac{\not2(3\pm2i)}{\not2} \\ \\x=3\pm2i$

d )

$x^2-x+4=0\\\Delta=(-1)^2-4.1.4\\\Delta=1-16\\\Delta=-15$

$x= \frac{1\pm \sqrt{-15} }{2} \\ \\x= \frac{1\pm~i \sqrt{15} }{2}$

Answer 2

a) x² + 25 = 0 ==> x² = - 25 ==> x= +/-√-25==> x= +/- √5i
============================================================
b) x² + 121 = 0 ==> x² = - 121 ==> x= +/-√-121==> x= +/- 11i
============================================================
c) x² - 6x + 13 = 0 

Δ = (-6)² - 4.1.13=36-52= - 16             √-16 = 4i

x= 6+/- 4i   ==> x= 2(3+/-2i) ==> x = 3 +/- 2i
        2                         2

==============================================================
d)   x² - x + 4 = 0 

Δ = (-1)² - 4.1.4= 1-16= -15            √-15 = √15i

x= 1+/-√15i   
           2