Question

URGENTEE HELPP

Sendo o complexo Z1 = (-1 + V3i)² , podemos dizer que Z1/2 é igual a?
A) -3 + √2i
B) 1 - 2i
C) -1 - √3i
D)√2i
E) -√3i

Answer 1

Z1 = (-1 + V3i)² = 1 -2√3i -3 = -2 -2√3i

Z1/2 = -2-2√3i/2 = -1 -√3i => c)

Answer 2

Explicação passo-a-passo:

$\sf z_1=(-1+\sqrt{3}\cdot i)^2$

$\sf z_1=(-1)^2+2\cdot(-1)\cdot\sqrt{3}\cdot i+(\sqrt{3}\cdot i)^2$

$\sf z_1=1-2\sqrt{3}\cdot i+3i^2$

$\sf z_1=1-2\sqrt{3}\cdot i+3\cdot(-1)$

$\sf z_1=1-2\sqrt{3}\cdot i-3$

$\sf z_1=1-3-2\sqrt{3}\cdot i$

$\sf z_1=-2-2\sqrt{3}\cdot i$

Assim:

$\sf \dfrac{z_1}{2}=\dfrac{-2-2\sqrt{3}\cdot i}{2}$

$\sf \red{\dfrac{z_1}{2}=-1-\sqrt{3}\cdot i}$

Letra C