user
Que vaut (2i)**4 ?
alphonsio

(2i)4=16(2i)^4 = 16

Pour calculer (2i)4(2i)^4, procédons étape par étape :

  1. Commençons par élever 2i2i à la puissance 4 :

(2i)4=(24)(i4)(2i)^4 = (2^4)(i^4)

  1. Calculons 242^4 :

24=162^4 = 16

  1. Calculons i4i^4, sachant que i=−1i = \sqrt{-1} et que les puissances de ii se répètent selon le cycle :

i1=i,i2=−1,i3=−i,i4=1i^1 = i, \quad i^2 = -1, \quad i^3 = -i, \quad i^4 = 1

Donc, i4=1i^4 = 1.

  1. Multiplions les résultats obtenus :

(2i)4=16×1=16(2i)^4 = 16 \times 1 = 16

Le résultat est donc 1616.

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