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If `alpha` is a non-real root of `x^6=1` then `(alpha^5+alpha^3+alpha+1)/(alpha^2+1) =`

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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE NUMERICAL ANSWER TYPE QUESTIONS
  1. Suppose a in R and z in C. "If" |z| = 2 and (z-alpha)/(z+alpha) is pur...

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  2. If alpha an d beta are roots of the equation x^(2)-2x+2=0, then the le...

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  3. Let S = {(2alpha+3i)/(2alpha-3i):alpha in R}. All the points of S lie ...

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  4. Let omega ne 1 be cube root of unity. Suppose (1 + omega)^(2023) = A +...

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  5. If (7+i)(z + bar(z))-(4+i)(z-bar(z)) + 116i = 0 then z bar(z) is equal...

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  6. Let C(1) be the curve represented by (2z + i)/(z-2) is purely imaginar...

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  7. Let a = 3 + 4i, z(1) and z(2) be two complex numbers such that |z(1)| ...

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  8. Let alpha be the real and beta, gamma be the complex roots of x^(3) + ...

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  9. Let z = ((2)/(i + sqrt(3)))^(200)+((2)/(i-sqrt(3)))^(200),"then" |z + ...

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  10. Let z be a non-zero complex number such that area of the triangle with...

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  11. Suppose x, y in R. If x^(2) + y + 4i is conjugate of -3 + x^(2) yi, th...

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  12. All the roots of the equation x^(11) - x^(6) - x^(5) + 1 = 0 lie on a ...

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  13. If 13 e^(i tan^(-1)(5//12))= a+ib, then |a| + |b| is equal to .

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  14. Suppose, a, b, c ge 0, c ne 1, a^(2) + b^(2) + c^(2) = c. If |(a+ib)/(...

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  15. Let z(1), z(2), z(3) be the roots of iz^(3) + 5z^(2) - z + 5i = 0, the...

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  16. Let S = {z in C : z^(2) = 4 (i bar(z))^(2)},"then" sum(z in S)|z+(1)/(...

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  17. Let z = (1)/(2) (sqrt(3) + i),"then" |(z^(101)+i^(103))^(105)|= .

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  18. If alpha = cos((8pi)/11)+i sin ((8pi)/11) then Re(alpha + alpha^2+alph...

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  19. Eccentricity of conic |z - 5i| + |z + 5i| = 25 is .

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  20. If alpha is a non-real root of x^6=1 then (alpha^5+alpha^3+alpha+1)/(a...

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