Citation :
-8 + 6i = (3 + i)²
Ah bon ?
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(1+i)z² + 3(-1+i)z -2-4i=0
Delta = (3(-1+i))² - 4(1+i)(-2-4i)
Delta = 9(1-1-2i) + 8 + 16i + 8i - 16
Delta = -8 + 6i
d = a + i.b
d² = -8+6i
a²-b²+2iab = -8 + 6i
a²-b² = -8
ab = 3
a²+b² = V(64+36) = 10
a²+b²+a²-b² = -8+10 = 2
2a² = 2
a² = 1
a = +/- 1
b = +/- 3
d = +/- (1 + 3i) (ce sont les racines carrées de Delta)
z = [-3(-1+i) +/- (1+3i)]/(2(1+i))
z1 = [-3(-1+i) - (1+3i)]/(2(1+i)) = (1 - 3i)/(1+i) = (1-3i)(1-i)/2 = (1-i-3i-3)/2 = - 1 - 2i
z2 = [-3(-1+i) + (1+3i)]/(2(1+i)) = 2/(1+i) = 1(1-i)/2 = 1-i
S : {-1-2i ; 1-i}
Sauf distraction.
