# For complex lovers

Algebra Level pending

Let $$\theta=|max(arg(Re(\frac{1}{z-i}).Re(z)+iIm(\frac{1}{z-i})))|$$

where $$|z|=1$$ and $$z \neq i$$ and $$w=e^{i \theta}$$,

if $$x=aw+bw^2+c , y=a+bw+cw^2 ,z=aw^2+b+cw$$ then

Find the value of $$|\frac{x^2+y^2+z^2+2ab+2bc+2ac}{a^2+b^2+c^2}|$$

(where $$a,b,c,x,y,z$$ are non zero complex numbers).

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