Question

1) Escreva os seguintes números complexos na forma trigonométrica:



A)z = i

B)z = 4

Answer 1

$z = i = 0 + 1i \\ \\ |z| = 1 \\ \\ \cos \theta = \frac{a}{ |z| } = \frac{0}{1} = 0 \\ \\ \sin \theta = \frac{b}{ |z| } = \frac{1}{1} = 1 \\ \\ \theta = \frac{\pi}{2} \\ \\ z = 1( \cos \frac{\pi}{2} + i \sin \frac{\pi}{2} )$

$z = 4= 4 + 0i \\ \\ |z| = 4 \\ \\ \cos \theta = \frac{a}{ |z| } = \frac{4}{4} = 1 \\ \\ \sin \theta = \frac{b}{ |z| } = \frac{0}{4} = 1 \\ \\ \theta = 0\\ \\ z = 4( \cos0+ i \sin0)$