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Sarah146
@Sarah146
May 2019
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Aider svp besoin pour lundi merci
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anylor
Bonjour
méthode : pour mettre un nombre complexe sous sa forme algébrique, on peut le multiplier par la quantité conjuguée.
ou développer (selon les cas)
a)
(5+2i)(3+i) =2i²+11i+15
=-2+11i+15
=13+11i
b)
-1/i = -1/i × i/i = -i/i² = -i/-1
=i
c)
(3-i)/(1+i) =(3-i)× (1-i)
/ (1+i)
×
(1-i)
=3-3i-i+i² / 1-i²
=3-4i-1 / 1 +1
=2-4i /2
= 1- 2i
d)
(1+i)^4
=(1+i)² ×(1+i)²
= (1+2i+i²) ×
(1+2i+i²)
= 1 +2i + i² +2i +4i² +2i³ +i²+2i³+i^4
= 1 +2i -1 +2i -4 -2i -1-2i +1
= - 4
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Lista de comentários
méthode : pour mettre un nombre complexe sous sa forme algébrique, on peut le multiplier par la quantité conjuguée.
ou développer (selon les cas)
a)
(5+2i)(3+i) =2i²+11i+15
=-2+11i+15
=13+11i
b)
-1/i = -1/i × i/i = -i/i² = -i/-1
=i
c)
(3-i)/(1+i) =(3-i)× (1-i) / (1+i) ×(1-i)
=3-3i-i+i² / 1-i²
=3-4i-1 / 1 +1
=2-4i /2
= 1- 2i
d)
(1+i)^4
=(1+i)² ×(1+i)²
= (1+2i+i²) × (1+2i+i²)
= 1 +2i + i² +2i +4i² +2i³ +i²+2i³+i^4
= 1 +2i -1 +2i -4 -2i -1-2i +1
= - 4