Q u a l d o s v a l o r e s i n d i c a d o s n a ~ o e ˊ arg ⁡ u m e n t o d e 1 − 3 i Qual\ dos\ valores\ indicados\ não\ é\ \arg umento\ de\ 1-\sqrt{3}i Q u a l d o s v a l o r e s i n d i c a d o s n a ~ o e ˊ ar g u m e n t o d e 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

− π 3 -\frac{\pi}{3} − 3 π

− 7 π 3 -\frac{7\pi}{3} − 3 7 π

Na forma trigonométrica, o complexo 2 ( s e n ( θ ) − i cos ⁡ ( θ ) ) 2\left(sen\left(\theta\right)-i\cos\left(\theta\right)\right) 2 ( s e n ( θ ) − i cos ( θ ) ) é

2 e i ( θ − π 2 ) 2e^{i\left(\theta-\frac{\pi}{2}\right)} 2 e i ( θ − 2 π )

e i ( θ − π 2 ) e^{i\left(\theta-\frac{\pi}{2}\right)} e i ( θ − 2 π )

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

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

Uma representação na forma trigonométrica de 3 − 3 ∑ k = 0 26 i k 3-3\sum_{k=0}^{26}i^k 3 − 3 k = 0 ∑ 2 6 i k é

3 2 e i ( 7 π 4 ) 3\sqrt{2}e^{i\left(\frac{7\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"> e i ( 4 7 π )

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

3 2 e i ( π 4 ) 3\sqrt{2}e^{i\left(\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"> e i ( 4 π )

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

Qual pode ser a representação algébrica do complexo e i ( 2 π 5 ) e^{i\left(\frac{2\pi}{5}\right)} e i ( 5 2 π )

5 − 1 4 + 5 + 5 4 i \frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i 4 5 <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 + 4 5 + 5 <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"> <path d="M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167, 158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067 c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84, 175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71 c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3, -252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26 s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z"> i

( 5 − 1 ) + ( 5 + 5 ) i \left(\sqrt{5}-1\right)+\left(\sqrt{5+\sqrt{5}}\right)i ( 5 <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 ) + ( 5 + 5 <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"> <path d="M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7, 572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7, -7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39 c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60 s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5, -658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z M1001 80H400000v40H1013z"> ) i

( 5 − 1 ) − ( 5 + 5 ) i \left(\sqrt{5}-1\right)-\left(\sqrt{5+\sqrt{5}}\right)i ( 5 <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 ) − ( 5 + 5 <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"> <path d="M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7, 572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7, -7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39 c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60 s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5, -658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z M1001 80H400000v40H1013z"> ) i

− 5 − 1 4 + 5 + 5 4 i -\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i − 4 5 <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 + 4 5 + 5 <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"> <path d="M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167, 158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067 c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84, 175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71 c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3, -252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26 s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z"> i

Qual é o valor de arg ⁡ ( − 6 − 18 i ) \arg\left(-\sqrt{6}-\sqrt{18}i\right) ar g ( − 6 <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 8 <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 ) ?

− 2 π 3 -\frac{2\pi}{3} − 3 2 π

− 5 π 6 -\frac{5\pi}{6} − 6 5 π

Sendo z 1 = 2 e i ( 6 π 5 ) e z 2 = − 1 + 3 i z_1=2e^{i\ \left(\frac{6\pi}{5}\right)}\ \ \ e\ \ \ z_2=-1+\sqrt{3}i z 1 = 2 e i ( 5 6 π ) e z 2 = − 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 qual o valor de arg ⁡ ( z 1 × z 2 i ) \arg\left(\frac{z_1\times z_2}{i}\right) ar g ( i z 1 × z 2 )

− 19 π 30 -\frac{19\pi}{30} − 3 0 1 9 π

11 π 30 \frac{11\pi}{30} 3 0 1 1 π

− 11 π 30 -\frac{11\pi}{30} − 3 0 1 1 π

19 π 30 \frac{19\pi}{30} 3 0 1 9 π

Complexos - Forma trigonométrica

Quiz

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

Manuela Simões

Used 5+ times

FREE Resource

10 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Considera os seguintes números complexos
$z_1=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i;\ z_2=\frac{5}{3+4i}$

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

z1 e z4

z1, z2 e z4

z1, z3 e z4

z1 e z2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$Qual\ dos\ valores\ indicados\ não\ é\ \arg umento\ de\ 1-\sqrt{3}i$

$\frac{8\pi}{3}$

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

$\frac{5\pi}{3}$

$-\frac{7\pi}{3}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

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

$e^{i\left(\theta+\frac{\pi}{2}\right)}$

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

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

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?

$\frac{5\pi}{4}$

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

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

$-\frac{\pi}{4}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Uma representação na forma trigonométrica de

$3-3\sum_{k=0}^{26}i^k$

é

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

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

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

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

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Qual pode ser a representação algébrica do complexo

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

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

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

$-\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i$

$\frac{\sqrt{5}-1}{4}+\frac{\sqrt{5+\sqrt{5}}}{4}i$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Qual é o valor de

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

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

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

$-\frac{5\pi}{6}$

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

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Complexos - Forma trigonométrica

10 questions

Considera os seguintes números complexos
$z_1=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i;\ z_2=\frac{5}{3+4i}$

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

$Qual\ dos\ valores\ indicados\ não\ é\ \arg umento\ de\ 1-\sqrt{3}i$

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

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

Uma representação na forma trigonométrica de

$3-3\sum_{k=0}^{26}i^k$

é

Qual pode ser a representação algébrica do complexo

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

Qual é o valor de

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

O afixo do número complexo

$e^{i\left(\frac{104\pi}{3}\right)}$ está em que quadrante?

Sendo

$z_1=2e^{i\ \left(\frac{6\pi}{5}\right)}\ \ \ e\ \ \ z_2=-1+\sqrt{3}i$

qual o valor de

$\arg\left(\frac{z_1\times z_2}{i}\right)$

Qual é o valor de

$\frac{\left(1+\sqrt{3}\right)^7}{e^{i\ \left(-\frac{\pi}{6}\right)}\times\left(1-\sqrt{3}i\right)^4}$

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Complexos - Forma trigonométrica

10 questions

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

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

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

Uma representação na forma trigonométrica de 3−3∑k=026ik3-3\sum_{k=0}^{26}i^k3−3k=0∑26​ik é

Qual pode ser a representação algébrica do complexo ei(2π5)e^{i\left(\frac{2\pi}{5}\right)}ei(52π​)

Qual é o valor de arg⁡(−6−18i)\arg\left(-\sqrt{6}-\sqrt{18}i\right)arg(−6​−18​i) ?

O afixo do número complexo ei(104π3)e^{i\left(\frac{104\pi}{3}\right)}ei(3104π​) está em que quadrante?

Sendo z1=2ei (6π5) e z2=−1+3iz_1=2e^{i\ \left(\frac{6\pi}{5}\right)}\ \ \ e\ \ \ z_2=-1+\sqrt{3}iz1​=2ei (56π​) e z2​=−1+3​i qual o valor de arg⁡(z1×z2i)\arg\left(\frac{z_1\times z_2}{i}\right)arg(iz1​×z2​​)

Qual é o valor de (1+3)7ei (−π6)×(1−3i)4\frac{\left(1+\sqrt{3}\right)^7}{e^{i\ \left(-\frac{\pi}{6}\right)}\times\left(1-\sqrt{3}i\right)^4}ei (−6π​)×(1−3​i)4(1+3​)7​

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$Qual\ dos\ valores\ indicados\ não\ é\ \arg umento\ de\ 1-\sqrt{3}i$

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

Uma representação na forma trigonométrica de

$3-3\sum_{k=0}^{26}i^k$

é

Qual pode ser a representação algébrica do complexo

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

Qual é o valor de

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

O afixo do número complexo

$e^{i\left(\frac{104\pi}{3}\right)}$ está em que quadrante?

Sendo

$z_1=2e^{i\ \left(\frac{6\pi}{5}\right)}\ \ \ e\ \ \ z_2=-1+\sqrt{3}i$

qual o valor de

$\arg\left(\frac{z_1\times z_2}{i}\right)$

Qual é o valor de

$\frac{\left(1+\sqrt{3}\right)^7}{e^{i\ \left(-\frac{\pi}{6}\right)}\times\left(1-\sqrt{3}i\right)^4}$