Considerando o número complexo w = − 2 − 5 i w\ =\ -2-5i w = − 2 − 5 i , qual das alternativas abaixo está correta?

R e ( w ) > I m ( w ) Re\left(w\right)>Im\left(w\right) R e ( w ) > I m ( w )

R e ( w ) = I m ( w ) Re\left(w\right)\ =\ Im\left(w\right) R e ( w ) = I m ( w )

R e ( w ) = − 2 e I m ( w ) = − 5 i Re\left(w\right)=-2\ e\ Im\left(w\right)=-5i R e ( w ) = − 2 e I m ( w ) = − 5 i

R e ( w ) < I m ( w ) Re\left(w\right)\ <Im\left(w\right) R e ( w ) < I m ( w )

Considerando o número complexo z ‾ = 1 + 3 2 i 2 \overline{z}\ =\ \frac{1+3\sqrt{2}i}{2} z = 2 1 + 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i , o número z + 1 2 z+\frac{1}{2} z + 2 1 pode ser representado por:

1 − 3 2 2 i 1-\frac{3\sqrt{2}}{2}i 1 − 2 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i

− 1 2 + 3 2 2 i -\frac{1}{2}+\frac{3\sqrt{2}}{2}i − 2 1 + 2 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i

1 + 3 2 2 i 1+\frac{3\sqrt{2}}{2}i 1 + 2 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i

− 3 2 2 i -\frac{3\sqrt{2}}{2}i − 2 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i

Sendo i i i a unidade imaginária, o resultado de ( 3 + 2 i ) ( 6 − 4 i ) − 1 + 3 i \frac{\left(3+2i\right)\left(6-4i\right)}{-1+3i} − 1 + 3 i ( 3 + 2 i ) ( 6 − 4 i ) é:

− 13 5 − 39 5 i -\frac{13}{5}-\frac{39}{5}i − 5 1 3 − 5 3 9 i

− 1 − 3 i -1-3i − 1 − 3 i

− 13 − 39 i -13-39i − 1 3 − 3 9 i

13 5 + 39 5 i \frac{13}{5}+\frac{39}{5}i 5 1 3 + 5 3 9 i

Math Championship - Números Complexos - Terceirão CMT

Authored by Patrick Guiesel

Mathematics

2nd Grade

Used 6+ times

Math Championship - Números Complexos - Terceirão CMT

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9 questions

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MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Qual é o conjugado do número complexo
$z\ =\ 2-5i$ ?

$-2+5i$

$2+5i$

$-5i+2$

$5i$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Qual é a parte imaginária do número complexo
$z\ =\ 2+3i$ ?

$2$

$3$

$-2$

$3i$

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

O quadrado da parte real do número complexo
$z\ =\ -5+4i$ é?

-25

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Considerando o número complexo
$w\ =\ -2-5i$ , qual das alternativas abaixo está correta?

$Re\left(w\right)\ =\ Im\left(w\right)$

$Re\left(w\right)=-2\ e\ Im\left(w\right)=-5i$

$Re\left(w\right)>Im\left(w\right)$

$Re\left(w\right)\ <Im\left(w\right)$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Os valores que tornam verdadeira a equação
$-18+pi\ =\ 3q-2i$ é:

$p=2\ e\ q=-6$

$p=-2\ e\ q=6$

$p=2\ e\ q=6$

$p=-2\ e\ q=-6$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Considerando o número complexo
$\overline{z}\ =\ \frac{1+3\sqrt{2}i}{2}$ , o número $z+\frac{1}{2}$ pode ser representado por:

$-\frac{1}{2}+\frac{3\sqrt{2}}{2}i$

$1-\frac{3\sqrt{2}}{2}i$

$1+\frac{3\sqrt{2}}{2}i$

$-\frac{3\sqrt{2}}{2}i$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Sendo $i$ a unidade imaginária, o resultado de $\frac{\left(3+2i\right)\left(6-4i\right)}{-1+3i}$ é:

$-1-3i$

$-\frac{13}{5}-\frac{39}{5}i$

$-13-39i$

$\frac{13}{5}+\frac{39}{5}i$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Para que $z=\frac{5+i}{a-2i}$ seja imaginário puro, qual deve ser o valor de a?

$\frac{2}{5}$

$0$

$-10$

$-\frac{2}{5}$

$10$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Sendo $i$ a unidade imaginária, simplificando-se a expressão $\frac{\left(3+i\right)^{71}.\left(3-i\right)^{30}}{\left(i-3\right)^{29}.\left(-3-i\right)^{70}}$ obtém-se:

$10$

$-8$

$8$

$-10$

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Math Championship - Números Complexos - Terceirão CMT

Qual é o conjugado do número complexo z = 2−5iz\ =\ 2-5iz = 2−5i ?

Qual é a parte imaginária do número complexo z = 2+3iz\ =\ 2+3iz = 2+3i ?

O quadrado da parte real do número complexo z = −5+4iz\ =\ -5+4iz = −5+4i é?

Considerando o número complexo w = −2−5iw\ =\ -2-5iw = −2−5i , qual das alternativas abaixo está correta?

Os valores que tornam verdadeira a equação −18+pi = 3q−2i-18+pi\ =\ 3q-2i−18+pi = 3q−2i é:

Considerando o número complexo z‾ = 1+32i2\overline{z}\ =\ \frac{1+3\sqrt{2}i}{2}z = 21+32​i​ , o número z+12z+\frac{1}{2}z+21​ pode ser representado por:

Sendo iii a unidade imaginária, o resultado de (3+2i)(6−4i)−1+3i\frac{\left(3+2i\right)\left(6-4i\right)}{-1+3i}−1+3i(3+2i)(6−4i)​ é:

Para que z=\frac{5+i}{a-2i}z=a−2i5+i​ seja imaginário puro, qual deve ser o valor de a?

Sendo iii a unidade imaginária, simplificando-se a expressão (3+i)71.(3−i)30(i−3)29.(−3−i)70\frac{\left(3+i\right)^{71}.\left(3-i\right)^{30}}{\left(i-3\right)^{29}.\left(-3-i\right)^{70}}(i−3)29.(−3−i)70(3+i)71.(3−i)30​ obtém-se:

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Qual é o conjugado do número complexo
$z\ =\ 2-5i$ ?

Qual é a parte imaginária do número complexo
$z\ =\ 2+3i$ ?

O quadrado da parte real do número complexo
$z\ =\ -5+4i$ é?

Considerando o número complexo
$w\ =\ -2-5i$ , qual das alternativas abaixo está correta?

Os valores que tornam verdadeira a equação
$-18+pi\ =\ 3q-2i$ é:

Considerando o número complexo
$\overline{z}\ =\ \frac{1+3\sqrt{2}i}{2}$ , o número $z+\frac{1}{2}$ pode ser representado por:

Sendo $i$ a unidade imaginária, o resultado de $\frac{\left(3+2i\right)\left(6-4i\right)}{-1+3i}$ é:

Para que $z=\frac{5+i}{a-2i}$ seja imaginário puro, qual deve ser o valor de a?

Sendo $i$ a unidade imaginária, simplificando-se a expressão $\frac{\left(3+i\right)^{71}.\left(3-i\right)^{30}}{\left(i-3\right)^{29}.\left(-3-i\right)^{70}}$ obtém-se: