Question

3) Qual é o argumento do complexo z = 2 + 2i?
a) 45°
b) 135°
C) 224°
d) 315°​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\sf z = a + bi$

$\mathsf{ |\:z\:| = \sqrt{a^2 + b^2} }$

$\mathsf{ |\:z\:| = \sqrt{2^2 + 2^2} } = \sqrt{4 + 4} = \sqrt{8} = \sqrt{2^2.2}$

$\mathsf{ |\:z\:| = 2\sqrt{2}}$

$\sf cos\:\Theta = \dfrac{a}{|\:z\:|} = \dfrac{2}{2\sqrt{2}} = \dfrac{\sqrt{2}}{2}$

$\sf sen\:\Theta = \dfrac{b}{|\:z\:|} = \dfrac{2}{2\sqrt{2}} = \dfrac{\sqrt{2}}{2}$

$\sf tg\:\Theta = \dfrac{sen\:\Theta}{cos\:\Theta}$

$\sf tg\:\Theta = \dfrac{\sqrt{2}}{2} \div \dfrac{\sqrt{2}}{2} = 1$

$\boxed{\boxed{\sf tg\:45\textdegree = 1}} \leftarrow \textsf{letra A}$