Help: (1 Viewer)

[umm what]

can somone solve this?

 

[Timske]

Is it z + 1/z = sqrt(z) or z + 1/z = sqrt(2) ?

 

[umm what]

nah man
its z + 1/z = 2cos theta

Is it z + 1/z = sqrt(z) or z + 1/z = sqrt(2) ?

 

[nightweaver066]

We know that if z = cistheta (i.e. |z| = 1),

z + 1/z = 2Re(z)

If |z| does not equal to 1, you won't get a real result when adding z + 1/z.

Let z = cistheta,

cistheta + 1/cistheta = 2costheta

2costheta = root2

costheta = (root2)/2
= 1/root2

Therefore theta = pi/4

We also know that z^n + 1/z^n = 2cosntheta

So z^10 + 1/z^10 = 2cos10(pi/4)

= 2cos(5pi/2)

= 2cos(pi/2)

= 0

 

[Timske]

oh right mx2 thread :L