Question

O valor de (1/2 + i . 3/2)²⁰ é?

Answer 1

Resposta:

(1/2)¹¹ +( i.3/2)¹¹

(1/2)¹¹ + i¹¹ . 3/2¹¹

i¹¹ = (-i)

(1/2)¹¹ - i(3/2)¹¹

mesmos expoente (¹¹) e base( 2). Repete a base

(-2i/2)¹¹

-1¹¹ = -i

:)

Answer 2

Resposta:

i=√(-1)

i²=-1

(1/2 + i√3/2)²⁰

z^n=|z|^n*[cos(n*θ)+i * sen(n*θ)]

z=1/2 + i√3/2

|z|=√[(1/2)²+(√3/2)²]

|z|=√[1/4+3/4] =1

tan(θ)= (√3/2)/(1/2)=√3   ==>θ=60°

(1/2 + i√3/2)²⁰ = 1²⁰ * [cos(20*60)+i * sen(20*60)]

(1/2 + i√3/2)²⁰ = cos(1200)+i * sen(1200)

***1200=>3*360+120

(1/2 + i√3/2)²⁰ = cos(120)+ i * sen(120)

cos(a+a)=2*cos²(a)-1

cos(120)=cos(60+60)=2*cos²(60)-1 =2*1/4-1 = -1/2

sen(a+a)=2*sen(a)*cos(a)

sen(120)=sen(60+60)=2*sen(60)*cos(60)=2*(√3/2) *1/2 =√3/2

(1/2 + i√3/2)²⁰ = -1/2+ i * √3/2

Letra E