Question

Observando o exemplo: resolvendo x²+4=0 solução>> x²+4=0 >> x²=-4 >> x=raiz de -4 utilizando os números complexos onde i=raiz -1 temos que x=raiz de -1 vezes raiz de 4 Logo x=+ou- 2i x= {+2i, -2i} Calcule: A) X²+9=0 B) X²+25=0 C) X²+400=0 D) X²+1=0 E) X²-6x+10=0

Answer 1

Explicação passo-a-passo:

a) $x^2+9=0$

$x^2=-9$

$x^2=9\cdot(-1)$

Lembrando que $i^2=-1$

$x^2=9i^2$

$x=\pm\sqrt{9i^2}$

$x=3i$ ou $x=-3i$

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

b) $x^2+25=0$

$x^2=-25$

$x^2=25\cdot(-1)$

$x^2=25i^2$

$x=\pm\sqrt{25i^2}$

$x=5i$ ou $x=-5i$

$S=\{-5i, 5i\}$

c) $x^2+400=0$

$x^2=-400$

$x^2=400\cdot(-1)$

$x^2=400i^2$

$x=\pm\sqrt{400i^2}$

$x=20i$ ou $x=-20i$

$S=\{-20i, 20i\}$

d) $x^2+1=0$

$x^2=-1$

$x^2=1\cdot(-1)$

$x^2=1i^2$

$x^2=i^2$

$x=\pm\sqrt{i^2}$

$x=i$ ou $x=-i$

$S=\{-i, i\}$

e) $x^2-6x+10=0$

$\Delta=(-6)^2-4\cdot1\cdot10$

$\Delta=36-40$

$\Delta=-4$

$\Delta=4\cdot(-1)$

$\Delta=4i^2$

$x=\dfrac{-(-6)\pm\sqrt{4i^2}}{2\cdot1}=\dfrac{6\pm2i}{2}$

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

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

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