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If alpha=e^(i2pi//7)a n df(x)=a0+sum(k-0...

If `alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k-0)^(20)a_k x^k ,` then prove that the value of `f(x)+f(alpha, x)++f(alpha^6x)` is independent of `alphadot`

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The correct Answer is:
`7A_0+7A_7x^7+7A_14x^14`
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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. Among the complex numbers z satisfying the condition |z+3-sqrt(3)i|=sq...

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  2. Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1), 'n' a positive integer ...

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  3. If alpha=e^(i2pi//7)a n df(x)=a0+sum(k-0)^(20)ak x^k , then prove that...

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  4. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

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  5. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

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  6. If n is a positive integer, prove the following (1+cos theta+i sin the...

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  7. If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n)...

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  8. Find all those roots of the equation z^12 – 56z^6 – 512 = 0 whose ima...

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  9. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

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  10. Solve (z-1)^4-16=0 . Find sum of roots. Locate roots, sum of roots and...

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  11. If omega is a non-real cube root of unity, then the value of (1-omega...

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  12. If omega is an imaginary cube root of unity then prove that If omeg...

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  13. If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1...

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  14. If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+...

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  15. If omega is a cube root of unity, then find the value of the following...

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  16. If =a+b,y=aomega+bomega^2 and z=aomega^2+bomega, prove tht xyz=a^3+b^3

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  17. If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an i...

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  18. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  19. (1+w)^7=A+Bw where w is the imaginary cube root of of a unity and A, B...

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  20. The value of the expression , (2-w)(2-w^2)+2.(3-w)(3-w^2)+....... .......

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