Question

√i = a + bi
i² = -1
quais os valores de a e b?​

Answer 1

Resposta:

V = { (-√2/2 ; -√2/2) , ( √2/2 ; √2/2) , ( i√2/2 ; -i√2/2) , (-i√2/2 ; i√2/2) }

i = (a +bi) ²

i = a ² -b ² + i. (2ab)

Sistema:

a ² - b ² = 0

2ab = 1

⇒

b = 1/2a

a² - (1/2a) ² = 0

a⁴ = 1/4

a = ∜ 1/4

⇒

a ₁ = -1/ √2

a ₂ = 1/ √2

a ₃ = i/ √2

a ₄ = -i/ √2

...

b ₁ = -√2/2

b ₂ = √2/2

b ₃ = -i√2/2

b ₄ = i√2/2