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Números Complexos

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Números Complexos

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Pequeno quiz sobre números complexos, criado no âmbito da unidade curricular OETDGSA

Created by

mariana varela
mariana varela
Portugal

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Números Complexos
 

Números ComplexosOnline version

Pequeno quiz sobre números complexos, criado no âmbito da unidade curricular OETDGSA

by mariana varela
1

Considere os números complexos z= -1-2i e k= 8-6i. Calcule k/z.

2

Quais são os valores de x para que o número complexo z = x + (x^2 - 1)i seja um número real?

3

Considere o triângulo equilátero [WBZ]. Os pontos B e Z são afixos dos números complexos z1e z2, respetivamente. O afixo do número complexo [(z1)^2]x(z2) pertence ao ____ quadrante.

4

Completa corretamente a frase: O _________ de um número complexo z = a + bi é w= a - bi.

Explicação

Aplicando o conjugado ao denominador, a fração fica da forma (-8+16i+6i-12i^2)/(1-4i^2). Como i^2=-1, o numerador é (-8+12 + 22i), enquanto que o denominador é (1+4), sendo B a resposta correta.

Um número complexo será real se a sua parte imaginária for igual a zero, logo, z será real se x^2-1=0 => x=1 V x=-1

Pela figura, z1 e z2 são complexos da forma z1=ai, z2=-b-c1, para a,b,c>0. Assim, tem-se (z1)^2= - a^2 <0 [(z1)^2]x(z2)= (a^2)b + (a^2)c, pelo que tanto a parte real tanto a imaginária são positivas. Então, o afixo pertencerá ao primeiro quadrante.

Geometricamente, no plano complexo, o conjugado é a reflexão do número original em relação ao eixo real. Assim, o conjugado de um número complexo da forma z=a+bi será obtido trocando o sinal da parte imaginária.

 
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