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Batvilcot
@Batvilcot
April 2019
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Bonjour aidez moi pour les questions 3 et 4 svp
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2)z²+ z + 1 = 0 delta = 1 - 4 = -3 or i²=-1 -3 = 3i² = ( i √3 )²
les solutions sont ( - 1 + i √3) /2 = -1/2 + i √3/2 = j
et ( - 1 - i √3) /2 = -1/2 - i √3/2 = conjugué de j
3)la question 2 a prouvé que 1 + j +j² = 0
la question 1 que j ³ -1 =(j -1)(j² + j +1)
de ces deux questions on déduit que j³ - 1 = ( j -1)( 0) = 0 puis que j³ = 1
4) de j² + j + 1 = 0 on déduit
j² = -j - 1 = -( - 1 + i √3) /2 -1 = 1/2 - i √3 /2 - 1 = -1/2 - i √3 = conjugué de j
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2)z²+ z + 1 = 0 delta = 1 - 4 = -3 or i²=-1 -3 = 3i² = ( i √3 )²les solutions sont ( - 1 + i √3) /2 = -1/2 + i √3/2 = j
et ( - 1 - i √3) /2 = -1/2 - i √3/2 = conjugué de j
3)la question 2 a prouvé que 1 + j +j² = 0
la question 1 que j ³ -1 =(j -1)(j² + j +1)
de ces deux questions on déduit que j³ - 1 = ( j -1)( 0) = 0 puis que j³ = 1
4) de j² + j + 1 = 0 on déduit
j² = -j - 1 = -( - 1 + i √3) /2 -1 = 1/2 - i √3 /2 - 1 = -1/2 - i √3 = conjugué de j