Question

last ? i need help on. Find the complex roots of 81[cos(3pi/8) + i sin(3pi/8)].

Use the fact that adding 2π to the angle (3pi/8) produces the same effective angle to generate the other three possible angles for the fourth roots. Be sure that your angles lie between 0 and 2π.

Answer 1

u already have
\[ z=\rho(\cos\theta+i\sin\theta) \]
where \(\rho=|z|\) and \(\theta=Arg(z)\)

Answer 2

kinda lost ?

Answer 3

when you have \(z=\rho(\cos\varphi+i\sin\varphi)\) then its n n-th roots are given by
\[ w_n=\sqrt[n]{\rho}\left[\cos\frac{\varphi+2k\pi}{n}+i\sin\frac{\varphi+2k\pi}{n}\right] \]