Réponse :

Explications étape par étape

Bonjour;

On a : cos(α) + sin(α) = √2(√2/2 cos(α) + √2/2 sin(α))

= √2(cos(π/4) cos(α) + sin(π/4) sin(α))

= √2cos(π/4 - α) ;

et : cos(α) - sin(α) = √2(√2/2 cos(α) - √2/2 sin(α))

= √2(sin(π/4) cos(α) - cos(π/4) sin(α))

= √2sin(π/4 - α) ;

donc : (cos(α) + sin(α)) + i (cos(α) - sin(α))

= √2cos(π/4 - α) + i √2sin(π/4 - α)

= √2(cos(π/4 - α) + i sin(π/4 - α))