( u + v ) n \left(u+v\right)^n ( u + v ) n

( u − v ) n \left(u-v\right)^n ( u − v ) n

( u + v ) k \left(u+v\right)^k ( u + v ) k

( u − v ) k \left(u-v\right)^k ( u − v ) k

Si z = a + i b z=a+ib z = a + i b alors z × z ‾ = z\times\overline{z}= z × z =

a ² + b ² a²+b² a ² + b ²

a ² + i b ² a²+ib² a ² + i b ²

a z ² + b z + c = 0 az²+bz+c=0 a z ² + b z + c = 0 , si Δ < 0 \Delta<0 Δ < 0 , alors les solutions sont :

− b − i ∣ Δ ∣ 2 a \frac{-b-i\sqrt{\left|\Delta\right|}}{2a} 2 a − b − i ∣ Δ ∣ <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">

− b + i ∣ Δ ∣ 2 a \frac{-b+i\sqrt{\left|\Delta\right|}}{2a} 2 a − b + i ∣ Δ ∣ <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">

− b − Δ 2 a \frac{-b-\sqrt{\Delta}}{2a} 2 a − b − Δ <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">

− b + ∣ Δ ∣ 2 a \frac{-b+\sqrt{\left|\Delta\right|}}{2a} 2 a − b + ∣ Δ ∣ <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">

z ² + 4 z + 13 = 0 z²+4z+13=0 z ² + 4 z + 1 3 = 0 , les solutions sont :

− 2 − 3 i -2-3i − 2 − 3 i et -2+3i − 2 + 3 i

2 + 3 i 2+3i 2 + 3 i et 2 − 3 i 2-3i 2 − 3 i

3 + 2 i 3+2i 3 + 2 i et 3 − 2 i 3-2i 3 − 2 i

− 3 − 2 i -3-2i − 3 − 2 i et − 3 + 2 i -3+2i − 3 + 2 i

Nombres complexes

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Mathematics

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9th Grade - Professional Development

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Practice Problem

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Medium

Sylvain DESHAYES

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12 questions

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FILL IN THE BLANK QUESTION

20 sec • 1 pt

La partie réelle de
$z=-4-2i$

FILL IN THE BLANK QUESTION

20 sec • 1 pt

La partie imaginaire de
$z=-4-2i$

FILL IN THE BLANK QUESTION

20 sec • 1 pt

La complexe conjugué de
$z=-4-2i$ est $\overline{z}=$

FILL IN THE BLANK QUESTION

20 sec • 1 pt

La partie réelle de
$z=28+3i$

FILL IN THE BLANK QUESTION

20 sec • 1 pt

La partie imaginaire de
$z=28+3i$

FILL IN THE BLANK QUESTION

20 sec • 1 pt

Le complexe conjugué de
$z=28+3i$ est $\overline{z}=$

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

est égale à

$\left(u+v\right)^n$

$\left(u-v\right)^n$

$\left(u+v\right)^k$

$\left(u-v\right)^k$

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