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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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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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  2. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

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  3. The maximum value of |a r g(1/(1-z))|for|z|=1,z!=1 is given by.

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

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  5. Let alpha and beta be real numbers and z be a complex number. If z^(2...

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  6. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

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

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  8. If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...

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

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  10. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2(y-y0)^2=...

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

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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. If z is a complex number such that |z|>=2 then the minimum value of |z...

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  15. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

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  16. Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2...

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

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  18. A value of theta for which (2+3isintheta)/(1-2isintheta) is purely ima...

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  19. Let 0 ne a, 0 ne b in R. Suppose S={z in C, z=1/(a+ibt)t in R, t ne ...

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  20. Let omega be a complex number such that 2omega+1=z where z=sqrt(-3). I...

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