Complexos - Forma trigonométrica

Complexos - Forma trigonométrica

12th Grade

10 Qs

quiz-placeholder

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Complexos - Forma trigonométrica

Complexos - Forma trigonométrica

Assessment

Quiz

Mathematics

12th Grade

Practice Problem

Hard

Created by

Manuela Simões

Used 5+ times

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10 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Considera os seguintes números complexos
 z1=22+22i; z2=53+4iz_1=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i;\ z_2=\frac{5}{3+4i} 

 z3=cos(π3)+isen(π6); z4=cos(π5)+isen(π5)z_3=\cos\left(\frac{\pi}{3}\right)+isen\left(\frac{\pi}{6}\right);\ z_4=\cos\left(\frac{\pi}{5}\right)+isen\left(\frac{\pi}{5}\right)  Quais são os complexos unitários?

z1 e z4

z1, z2 e z4

z1, z3 e z4

z1 e z2

2.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

 Qual dos valores indicados na~o eˊ argumento de 13iQual\ dos\ valores\ indicados\ não\ é\ \arg umento\ de\ 1-\sqrt{3}i  

 8π3\frac{8\pi}{3}  

 π3-\frac{\pi}{3}  

 5π3\frac{5\pi}{3}  

 7π3-\frac{7\pi}{3}  

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

 Na forma trigonométrica, o complexo
 2(sen(θ)icos(θ))2\left(sen\left(\theta\right)-i\cos\left(\theta\right)\right)  
é



 ei(θπ2)e^{i\left(\theta-\frac{\pi}{2}\right)}  

 ei(θ+π2)e^{i\left(\theta+\frac{\pi}{2}\right)}  

 2ei(θ+π2)2e^{i\left(-\theta+\frac{\pi}{2}\right)}  

 2ei(θπ2)2e^{i\left(\theta-\frac{\pi}{2}\right)}  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Os complexos, não nulos, com afixo na bissetriz do 3º quadrante têm argumento principal igual a que valor?

5π4\frac{5\pi}{4}

3π4\frac{3\pi}{4}

3π4-\frac{3\pi}{4}

π4-\frac{\pi}{4}

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Uma representação na forma trigonométrica de

 33k=026ik3-3\sum_{k=0}^{26}i^k  

é

 3ei(7π4)3e^{i\left(\frac{7\pi}{4}\right)}  

 32ei(7π4)3\sqrt{2}e^{i\left(\frac{7\pi}{4}\right)}  

 32ei(π4)3\sqrt{2}e^{i\left(\frac{\pi}{4}\right)}  

 3ei(π4)3e^{i\left(\frac{\pi}{4}\right)}  

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Qual pode ser a representação algébrica do complexo

 ei(2π5)e^{i\left(\frac{2\pi}{5}\right)}  

 (51)+(5+5)i\left(\sqrt{5}-1\right)+\left(\sqrt{5+\sqrt{5}}\right)i  

 (51)(5+5)i\left(\sqrt{5}-1\right)-\left(\sqrt{5+\sqrt{5}}\right)i  

 514+5+54i-\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i  

 514+5+54i\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i  

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Qual é o valor de

 arg(618i)\arg\left(-\sqrt{6}-\sqrt{18}i\right)  ?

 4π3\frac{4\pi}{3}  

 2π3\frac{2\pi}{3}  

 5π6-\frac{5\pi}{6}  

 2π3-\frac{2\pi}{3}  

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