Complex no proof question (1 Viewer)

[Aysce]

If a+ib = [(x+i)^2] / 2x-i prove a^2 + b^2 = [(x^2 +1)^2] / 4x^2 +1. Thanks guys sorry im on the phone

 

[nightweaver066]

or

 

[Aysce]

or

2x -i

 

[darkphoenix]

(a+ib)(a-ib)=a^2+b^2

a+ib= (x+i)^2/2x-i there for a-ib= (x-i)^2/2x+i (conjugate)

times each other give u : (x^2+1)(x^2+1)/4x^2+1
which equals to (x^2+1)^2/4x^2+1

 

[Aysce]

Thanks so much man

 

[Aysce]

Can someone please help me with complex roots of unity, I've been stuck on this for ages..

Q. If w is a complex cube root of unity, show that:

(a+ bw + cw^2) / (c + aw + bw^2) = 0.

 

[seanieg89]

 

[Aysce]

SHIT! My bad RHS = w^2 .... =.=

 

[seanieg89]