Question

Sendo o módulo !Z! = 10 e o argumento Z = (5π/3). Indique o número complexo na forma algébrica. a) Z = – 5 – √3i b) Z = + 5 – 5√3i c) Z = + 3 + 3√5i d) Z = – 5 + 5√3i

Answer 1

Resposta:

$\text{letra B}$

Explicação passo-a-passo:

$|\text{ z }| = 10$

$\text{cos }\Theta = \dfrac{\text{a}}{|\text{ z }|}$

$\text{cos }\dfrac{5\pi }{3} = \dfrac{\text{a}}{|\text{ z }|}$

$\dfrac{\text{a}}{10} = \dfrac{1}{2}$

$\boxed{\boxed{a = 5}}$

$\text{sen }\Theta = \dfrac{\text{b}}{|\text{ z }|}$

$\text{sen }\dfrac{5\pi }{3} = \dfrac{\text{b}}{|\text{ z }|}$

$\dfrac{\text{b}}{10} = -\dfrac{\sqrt{3}}{2}$

$\boxed{\boxed{b = -5\sqrt{3}}}$

$\boxed{\boxed{\text{z } = 5 - 5\sqrt{3}i}}$