Komplexní čísla - goniometrický tvar

Komplexní čísla - goniometrický tvar

1st - 12th Grade

10 Qs

quiz-placeholder

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Komplexní čísla - goniometrický tvar

Komplexní čísla - goniometrický tvar

Assessment

Quiz

Mathematics

1st - 12th Grade

Hard

Created by

Zuzana Martincová

Used 7+ times

FREE Resource

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Podíl komplexních čísel 
 z1=4(cos300°+ i.sin 300°)z_1=4\left(\cos300°+\ i.\sin\ 300°\right)   z2=2(cos 30°+i.sin 30°)z_2=2\left(\cos\ 30°+i.\sin\ 30°\right)  
je

-2i

4i

-0,5i

i

jiná odpověď

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

 Algebraický tvar čísla 2(cos 34π+i.sin34π)2\left(\cos\ \frac{3}{4}\pi+i.\sin\frac{3}{4}\pi\right) je

 2+i2-\sqrt{2}+i\sqrt{2}  

 2i2\sqrt{2}-i\sqrt{2}  

 22i2-2i  

 2+2i2+2i  

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Goniometrický tvar čísla 12+i.32-\frac{1}{2}+i.\frac{\sqrt{3}}{2}   
je

 cos53π+i.sin53π\cos\frac{5}{3}\pi+i.\sin\frac{5}{3}\pi  

 cos23π+i.sin23π\cos\frac{2}{3}\pi+i.\sin\frac{2}{3}\pi  

 cos13π+i.sin13π\cos\frac{1}{3}\pi+i.\sin\frac{1}{3}\pi  

 cos32π+i.sin32π\cos\frac{3}{2}\pi+i.\sin\frac{3}{2}\pi  

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Součin čísel 

 a=3(cos13π+i.sin13π)a=3\left(\cos\frac{1}{3}\pi+i.\sin\frac{1}{3}\pi\right)  b=2(cos23π+i.sin23π)b=\sqrt{2}\left(\cos\frac{2}{3}\pi+i.\sin\frac{2}{3}\pi\right)  
je

 32(cos π2+i.sin π2)3\sqrt{2}\left(\cos\ \frac{\pi}{2}+i.\sin\ \frac{\pi}{2}\right)  

 32(cos π2+i.sin π2)-3\sqrt{2}\left(\cos\ \frac{\pi}{2}+i.\sin\ \frac{\pi}{2}\right)  

 32-3\sqrt{2}  

 323\sqrt{2}  

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Media Image

Které komplexní číslo je na obrázku?

22(cos 34π+i.sin34π)2\sqrt{2}\left(\cos\ \frac{3}{4}\pi+i.\sin\frac{3}{4}\pi\right)

22(cos 14π+i.sin14π)2\sqrt{2}\left(\cos\ \frac{1}{4}\pi+i.\sin\frac{1}{4}\pi\right)

22(cos 54π+i.sin54π)2\sqrt{2}\left(\cos\ \frac{5}{4}\pi+i.\sin\frac{5}{4}\pi\right)

22(cos 74π+i.sin74π)2\sqrt{2}\left(\cos\ \frac{7}{4}\pi+i.\sin\frac{7}{4}\pi\right)

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Goniometrický tvar komplexního čísla z = -2i je:

2(cos 0°+ i.sin 0°)

2(cos 90°+ i.sin 90°)

2(cos 180°+ i.sin 180°)

2(cos 270°+ i.sin 270°)

Jiná odpověď

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Goniometrický tvar komplexního čísla z = -3-3i je:

 32(cos45°+ i.sin 45°)3\sqrt{2}\left(\cos45°+\ i.\sin\ 45°\right)  

 32(cos135°+ i.sin 135°)3\sqrt{2}\left(\cos135°+\ i.\sin\ 135°\right)  

 32(cos225°+ i.sin 225°)3\sqrt{2}\left(\cos225°+\ i.\sin\ 225°\right)  

 32(cos315°+ i.sin 315°)3\sqrt{2}\left(\cos315°+\ i.\sin\ 315°\right)  

Jiná odpověď

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