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Komplexní čísla - goniometrický tvar

Authored by Zuzana Martincová

Mathematics

1st - 12th Grade

Used 10+ times

Komplexní čísla - goniometrický tvar
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10 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Podíl komplexních čísel 
 z1=4(cos⁡300°+ 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.sin⁡34π)2\left(\cos\ \frac{3}{4}\pi+i.\sin\frac{3}{4}\pi\right) je

 −2+i2-\sqrt{2}+i\sqrt{2}  

 2−i2\sqrt{2}-i\sqrt{2}  

 2−2i2-2i  

 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

 cos⁡53π+i.sin⁡53π\cos\frac{5}{3}\pi+i.\sin\frac{5}{3}\pi  

 cos⁡23π+i.sin⁡23π\cos\frac{2}{3}\pi+i.\sin\frac{2}{3}\pi  

 cos⁡13π+i.sin⁡13π\cos\frac{1}{3}\pi+i.\sin\frac{1}{3}\pi  

 cos⁡32π+i.sin⁡32π\cos\frac{3}{2}\pi+i.\sin\frac{3}{2}\pi  

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Součin čísel 

 a=3(cos⁡13π+i.sin⁡13π)a=3\left(\cos\frac{1}{3}\pi+i.\sin\frac{1}{3}\pi\right) ;  b=2(cos⁡23π+i.sin⁡23π)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.sin⁡34π)2\sqrt{2}\left(\cos\ \frac{3}{4}\pi+i.\sin\frac{3}{4}\pi\right)

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

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

22(cos⁡ 74π+i.sin⁡74π)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(cos⁡45°+ i.sin⁡ 45°)3\sqrt{2}\left(\cos45°+\ i.\sin\ 45°\right)  

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

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

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

Jiná odpověď

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