Numere complexe forma trigonometrică

Numere complexe forma trigonometrică

10th Grade

7 Qs

quiz-placeholder

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Numere complexe forma trigonometrică

Numere complexe forma trigonometrică

Assessment

Quiz

Mathematics

10th Grade

Hard

Created by

Maria Laura Popa

Used 5+ times

FREE Resource

7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Forma algebrică a numărului complex

 z =7(cos 11π6+isin 11π6) z\ =7\cdot\left(\cos\ \frac{11\pi}{6}+i\cdot\sin\ \frac{11\pi}{6}\right)\   este:

 732i72\frac{7\sqrt{3}}{2}-i\cdot\frac{7}{2}  

 732+i72\frac{7\sqrt{3}}{2}+i\cdot\frac{7}{2}  

  732 i72-\ \frac{7\sqrt{3}}{2}\ -i\cdot\frac{7}{2}  

 732+i72-\frac{7\sqrt{3}}{2}+i\cdot\frac{7}{2}  

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Forma trigonometrică a numărului complex

 z = 33iz\ =\ \sqrt{3}-3\cdot i  este:

 23(cos 2π3+isin 2π3)2\cdot\sqrt{3}\cdot\left(\cos\ \frac{2\pi}{3}+i\cdot\sin\ \frac{2\pi}{3}\right)  

 23(cos 5π3+isin 5π3)2\cdot\sqrt{3}\cdot\left(\cos\ \frac{5\pi}{3}+i\cdot\sin\ \frac{5\pi}{3}\right)  

 12(cos 5π6+isin 5π6)\sqrt{12}\cdot\left(\cos\ \frac{5\pi}{6}+i\cdot\sin\ \frac{5\pi}{6}\right)  

 12(cos 5π4+sin 5π4)\sqrt{12}\cdot\left(\cos\ \frac{5\pi}{4}+\sin\ \frac{5\pi}{4}\right)  

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Produsul

 5(cos π4+isin π4)\sqrt{5}\cdot\left(\cos\ \frac{\pi}{4}+i\cdot\sin\ \frac{\pi}{4}\right)  \cdot    20(cos 7π4+isin 7π4)\sqrt{20}\cdot\left(\cos\ \frac{7\pi}{4}+i\cdot\sin\ \frac{7\pi}{4}\right)  este:

 10(cos π4+isin π4)10\cdot\left(\cos\ \frac{\pi}{4}+i\cdot\sin\ \frac{\pi}{4}\right)  

 10i10\cdot i  

 1010  

 25(cos 2π+isin 2π)\sqrt{25}\cdot\left(\cos\ 2\pi+i\cdot\sin\ 2\pi\right)  

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Rezultatul calculului  (cos 5π6+isin 5π6) 24\left(\cos\ \frac{5\pi}{6}+i\cdot\sin\ \frac{5\pi}{6}\right)^{\ 24}  este:

 cos 29π6+isin 29π6\cos\ \frac{29\pi}{6}+i\cdot\sin\ \frac{29\pi}{6}  

  1-\ 1  

 cos0isin0\cos0-i\cdot\sin0  

1

5.

MULTIPLE CHOICE QUESTION

5 mins • 5 pts

6.

MULTIPLE CHOICE QUESTION

5 mins • 5 pts

7.

MULTIPLE CHOICE QUESTION

30 sec • 5 pts

Triunghiul ABC cu afixele vârfurilor

 zA=1+iz_A=1+i ,  zB=1+5iz_B=1+5\cdot i ,  zC=6+iz_C=6+i  este:

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