Il modulo e l'anomalia del numero complesso 1 + 3 i 1+\sqrt{3}i 1 + 3 <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 sono rispettivamente

2 ; π 3 2;\frac{\pi}{3} 2 ; 3 π

2 ; − π 3 2;\ -\frac{\pi}{3} 2 ; − 3 π

2 ; π 6 2;\frac{\pi}{6} 2 ; 6 π

Le coordinate polari del punto P sono [ 3 2 ; π 4 ] \left[3\sqrt{2};\frac{\pi}{4}\right] [ 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"> ; 4 π ] . Quali sono le sue coordinate cartesiane.

( 3 , 3 ) \left(3,3\right) ( 3 , 3 )

\left(3\sqrt{2},1\right) ( 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"> , 1 )

( − 3 , 3 ) \left(-3,3\right) ( − 3 , 3 )

( 3 2 , 3 2 ) \left(3\sqrt{2},3\sqrt{2}\right) ( 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"> , 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"> )

Quanto vale il rapporto 1 − i 2 + i \frac{1-i}{2+i} 2 + i 1 − i

1 5 − 3 5 i \frac{1}{5}-\frac{3}{5}i 5 1 − 5 3 i

La forma trigonometrica del numero complesso − 2 2 + 2 2 i -\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i − 2 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"> + 2 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 è:

cos ⁡ 3 4 π + i sin ⁡ 3 4 π \cos\ \frac{3}{4}\pi+i\sin\ \frac{3}{4}\pi cos 4 3 π + i sin 4 3 π

cos ⁡ 5 4 π + i sin ⁡ 5 4 π \cos\ \frac{5}{4}\pi+i\sin\ \frac{5}{4}\pi cos 4 5 π + i sin 4 5 π

cos ⁡ π 4 + i sin ⁡ π 4 \cos\ \frac{\pi}{4}+i\sin\ \frac{\pi}{4} cos 4 π + i sin 4 π

cos ⁡ 7 4 π + i sin ⁡ 7 4 π \cos\ \frac{7}{4}\pi+i\sin\ \frac{7}{4}\pi cos 4 7 π + i sin 4 7 π

determina il risultato della seguente moltiplicazione: 3 ( cos ⁡ π 6 + i s e n π 6 ) ⋅ 2 ( cos ⁡ π 3 + i s e n π 3 ) 3\left(\cos\frac{\pi}{6}+i\ sen\ \frac{\pi}{6}\right)\cdot2\left(\cos\ \frac{\pi}{3}+i\ sen\ \frac{\pi}{3}\right) 3 ( cos 6 π + i s e n 6 π ) ⋅ 2 ( cos 3 π + i s e n 3 π )

1 − 3 i 1-\sqrt{3}\ i 1 − 3 <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

Numeri complessi - D

Authored by Stefano Tomassucci

Mathematics

10th - 12th Grade

Used 5+ times

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15 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

La parte reale del numero 7i+3 è

-3

-7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

La rappresentazione del numero z=3 - 2i nel piano di Gauss è:

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Semplifica:
(10+ 15i)-(48 - 30i)

58 - 45i

58 - 15i

-38 - 15i

-38 + 45i

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Semplifica:
(7 + 2i)(9 - 6i)

75-24i

63 - 24i + 12i²

51 - 24i

58 + 60i

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Quanto vale $\sqrt{-100}$

-10

10i

-10i

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Moltiplica (2i)(3i)

-5

-6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Quale numero complesso corrisponde al punto C?

2 + i

-3

-1 - i

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Il modulo e l'anomalia del numero complesso $1+\sqrt{3}i$ sono rispettivamente

$2;\frac{\pi}{3}$

$4;\frac{\pi}{3}$

$2;\ -\frac{\pi}{3}$

$2;\frac{\pi}{6}$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Le coordinate polari del punto P sono $\left[3\sqrt{2};\frac{\pi}{4}\right]$ . Quali sono le sue coordinate cartesiane.

$\left(3\sqrt{2},1\right)$

$\left(3,3\right)$

$\left(-3,3\right)$

$\left(3\sqrt{2},3\sqrt{2}\right)$

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Numeri complessi - D

La parte reale del numero 7i+3 è

La rappresentazione del numero z=3 - 2i nel piano di Gauss è:

Semplifica:(10+ 15i)-(48 - 30i)

Semplifica:(7 + 2i)(9 - 6i)

Quanto vale −100\sqrt{-100}−100​

Moltiplica (2i)(3i)

Quale numero complesso corrisponde al punto C?

Calcola i7

Il modulo e l'anomalia del numero complesso 1+3i1+\sqrt{3}i1+3​i sono rispettivamente

Le coordinate polari del punto P sono [32;π4]\left[3\sqrt{2};\frac{\pi}{4}\right][32​;4π​] . Quali sono le sue coordinate cartesiane.

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Semplifica:
(10+ 15i)-(48 - 30i)

Semplifica:
(7 + 2i)(9 - 6i)

Quanto vale $\sqrt{-100}$

Calcola i⁷

Il modulo e l'anomalia del numero complesso $1+\sqrt{3}i$ sono rispettivamente

Le coordinate polari del punto P sono $\left[3\sqrt{2};\frac{\pi}{4}\right]$ . Quali sono le sue coordinate cartesiane.