um numero complexo variavel tem,para a parte real, os valores
e para parte imaginaria ![x\sqrt[]{2}](/latexrender/pictures/72ae2b5c4db703ef121fb4972aa73f34.png "x\sqrt[]{2}")
.qual o valor minimo do modulo desse numero?
por adauto martins » Ter Out 15, 2019 23:41
e para parte imaginaria .qual o valor minimo do modulo desse numero?
por adauto martins » Ter Out 15, 2019 23:54
![z=({x}^{2}-2)+(x\sqrt[]{2})i](/latexrender/pictures/615d8bb58a5fb426a800d28e83bf3e04.png "z=({x}^{2}-2)+(x\sqrt[]{2})i")
![\left|z \right|=\sqrt[]{{({x}^{2}-2)}^{2}+({x\sqrt[]{2}}^{2})}...](/latexrender/pictures/d9d5cee7c6bd1b607eca8c36c370cdf3.png "\left|z \right|=\sqrt[]{{({x}^{2}-2)}^{2}+({x\sqrt[]{2}}^{2})}...")
![\left|z \right|=\sqrt[]{{x}^{4}-2{x}^{2}-1}](/latexrender/pictures/cbc3a2b48c4c3f017cae9b708c9dcccb.png "\left|z \right|=\sqrt[]{{x}^{4}-2{x}^{2}-1}")
![d/x(\left|z \right|)=(-1/2)(\sqrt[]{(4{x}^{3}-4x})/({x}^{4}-2x+4)=0
\Rightarrow 4x(x-1)\Rightarrow x=1](/latexrender/pictures/22cb2ec9e0308bbca36100b0abbdfa36.png "d/x(\left|z \right|)=(-1/2)(\sqrt[]{(4{x}^{3}-4x})/({x}^{4}-2x+4)=0
\Rightarrow 4x(x-1)\Rightarrow x=1")
![(\left|z \right|)=\sqrt[]{1-2+4}=\sqrt[]{3}](/latexrender/pictures/fe4dfeef1179c7d4f1b20e8a4b028c96.png "(\left|z \right|)=\sqrt[]{1-2+4}=\sqrt[]{3}")
por adauto martins » Qua Out 16, 2019 17:24
![(d/dx)\left|z \right|=(1/2).(4.{x}^{3}-4x)/(\sqrt[]{({x}^{4}-2x1)}](/latexrender/pictures/5b5a4b93915b78aee4153f7728aa8385.png "(d/dx)\left|z \right|=(1/2).(4.{x}^{3}-4x)/(\sqrt[]{({x}^{4}-2x1)}")
é negativa(ponto de minimo)Usuários navegando neste fórum: Nenhum usuário registrado e 1 visitante
![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
(dica : igualar a expressão a 
e elevar ao quadrado os dois lados)