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Let omega=e^(ipi/3),and a,b,c,x,y,z be n...

Let `omega=e^(ipi/3)`,and a,b,c,x,y,z be non zero complex numbers such that `a+b+c=x`
`a+bomega+comega^2=y`
`a+bomega^2+comega=z` then the value of `(absx^2+absy^2+absz^2)/(absa^2+absb^2+absc^2)` is

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
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  2. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

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  3. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

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  4. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

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  5. If z is a complex number of unit modulus and argument theta then arg(...

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  6. Let z1=2+3i and z2=3+4i be two points on the complex plane then the se...

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  7. Suppose z=x+iy where x and y are real numbers and i=sqrt(-1) the point...

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  8. If P,Q,R are angles of an isosceles triangle and anglep=pi/2 then the ...

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  9. Let z be a complex number such that the imaginary part of z is non zer...

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  10. If z ne 1 and (z^2)/(z-1) is real then the point represented by the co...

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  11. The maximum value of absz when the complex number z satisfies the cond...

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  12. If (3/2+isqrt3/2)^50=3^25(x+iy)where x and y are real then the order P...

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  13. If (z-1)/(z+1) is purely imaginary then

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  14. The points representing the complex number z for which arg((z-2)/(z+2)...

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  15. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

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  16. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

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  17. If omega(ne1) is a cube root of unity and (1+omega)^7=A+Bomega then (A...

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  18. For the real parameter t,the locus of the complex number z=(1-t^2)+isq...

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  19. If x+(1/x)=2costheta then for any integer n,x^n+1/x^n=

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  20. If omega ne1 is a cube root of unity then the sum of the series S=1+2o...

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