Ivan Shishkin, Rye (1878)

Problems/Complex analysisExercise

Parties réelle et imaginaire de nombres complexe 2

by SalixBabylonica·
16
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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ReviewedReviewed by Sequoia
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Déterminer la partie imaginaire des nombres complexes suivants :

  1. z1=5+i−9+6iz_1 = 5+i-9+6i
  2. z2=(3+i)2z_{2}=(3+i)^{2}
  3. z3=(2i)3+5+i2z_{3}=(2i)^{3}+5+i^{2}
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Solution by SalixBabylonica

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On a :

  1. z1=−4+7iz_1 = -4+7i donc Re⁡(z1)=−4\Re(z_1)=-4 et Im⁡(z1)=7\Im(z_1) = 7
  2. z2=32+2×3i+i2=9+6i−1=8+6iz_2=3^2+2\times3i+i^2 = 9+6i-1 = 8+6i donc Re⁡(z2)=8\Re(z_2)=8 et Im⁡(z2)=6\Im(z_2) = 6
  3. z3=8i2×i+5+(−1)=−8i+4z_3=8i^2\times i+5+(-1) = -8i + 4 donc Re⁡(z3)=4\Re(z_3)=4 et Im⁡(z3)=−8\Im(z_3) = -8
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