Question

Seja o número complexo z= 2 (cos 150° + isen 150°). Determine z⁴ na forma de algébrica: ​

Answer 1

z= 2 (cos 150° + isen 150°).

cos 150=cos(180-30) =

cos180*cos30+sen180*sen30

=-cos30 =-√3/2

sen150=sen(180-30)=sen180*cos30-sen30 * cos180 =sen30=1/2

z = 2 *(-√3/2 +i/2)

z = -√3+i

z⁴=[(-√3+i)²]²

z⁴=[3 -2i√3+i²]²

z⁴=[3 -2i√3-1]²

z⁴=[2 -2i√3]² = 4 -8i√3+(2i√3)²

z⁴ = 4 -8i√3-12

z⁴ = -8i√3 - 8