Question

Escreva na forma algébrica:
a)z=[√8.(cos3π\4+ i.sen3π\4)]
b)z=[10.(cosπ\4+ i.sen2π\4)]

Answer 1

$a=\sqrt{8}.\cos(\dfrac{3\pi}{4})\\a=\sqrt{8}. -\dfrac{\sqrt{2}}{2}=-\dfrac{\sqrt{16}}{2}=-\dfrac{4}{2}=-2$

$b=\sqrt{8}.\sin(\dfrac{3\pi}{4})=\sqrt{8}.\dfrac{\sqrt{2}}{2}=2$

$\mathsf{z=a+bi} \\\mathsf{z=-2+2i}$

b)

$a=10.\cos(\dfrac{\pi}{4})=10.\dfrac{\sqrt{2}}{2}=5\sqrt{2}$

$b=10.\sin(\dfrac{\pi}{4})=10\dfrac{\sqrt{2}}{2}=5\sqrt{2}$

$\mathsf{z=a+bi} \\\mathsf{z=5\sqrt{2}+5\sqrt{2}i}$