Question

O valor de (1 – i)^8 é: *
a) 8
b) 16
c) 24
d) -16
e) -8

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(1 - i)^8}$

$\mathsf{\rho = \sqrt{a^2 + b^2}}$

$\mathsf{\rho = \sqrt{(1)^2 + (-1)^2}}$

$\mathsf{\rho = \sqrt{1 + 1}}$

$\mathsf{\rho = \sqrt{2}}$

$\mathsf{sen\:\Theta = \dfrac{b}{\rho} = \dfrac{-1}{\sqrt{2}} = -\dfrac{\sqrt{2}}{2}}$

$\mathsf{cos\:\Theta = \dfrac{a}{\rho} = \dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}}$

$\mathsf{\Theta = 315\textdegree = \dfrac{7\pi }{4}}$

$\mathsf{(1 - i) = \sqrt{2}\left(cos\:\dfrac{7\pi }{4} + i\:sen\:\dfrac{7\pi }{4}\right)}$

$\mathsf{(1 - i)^8 = (\sqrt{2})^8\left(cos\:\dfrac{7\pi.8 }{4} + i\:sen\:\dfrac{7\pi .8 }{4}\right)}$

$\mathsf{(1 - i)^8 = 16\left(cos\:14 \pi + i\:sen\: 14 \pi)}$

$\mathsf{(1 - i)^8 = 16\left(1 + i.0)}$

$\boxed{\boxed{\mathsf{(1 - i)^8 = 16}}}\leftarrow\textsf{letra B}$