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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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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. a ,b ,a n d c are all different and non-zero real numbers on arithmet...

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  2. Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R , then the number of possible i...

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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. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  5. If z is a non real root of root(7)(-1) , then find the value of z^(86...

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  6. The quadratic equation x^2+m x+n=0 has roots which are twice those of ...

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  7. Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1]...

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  8. All the value of k for which the quadratic polynomial f(x)=2x^2+k x+2=...

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  9. If a=cos(2pi//7)+isin(2pi//7), then find the quadratic equation whose ...

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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. If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary ...

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  12. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

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  13. Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=...

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  14. The value of i^(1+3+5+.....+(2n+1)) is.

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  15. a ,b , c are integers, not all simultaneously equal, and omega is cube...

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  16. a, b, c are reals such that a+b+c=3 and   1/(a+b)+ 1/(b+c) + 1/ (c+...

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  17. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

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  18. If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , ...

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  19. The locus of z which lies in shaded region (excluding the boundaries) ...

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  20. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

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