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

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 `(|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)`

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`0003`
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MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
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  2. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

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  3. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

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  4. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  5. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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  6. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  7. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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  8. Let z be a complex number such that the imaginary part of z is nonzero...

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  9. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

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  10. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

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  11. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

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  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  14. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

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  15. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

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  16. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

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  17. Let P=[{:((-z)^r,z^(2r)),(z^(2r),z^r):}] and Ibe the identity matrix o...

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  18. Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the co...

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  19. Let s ,\ t ,\ r be non-zero complex numbers and L be the set of ...

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  20. For a non-zero complex number z , let arg(z) denote the principal ar...

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