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If 1,a1,a2,a3,…,a(n-1) are the nth roots...

If 1,`a_1,a_2,a_3`,…,`a_(n-1)` are the nth roots of unity then prove that : `(1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1))`=n.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a0+a3+a6+a9+… .

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  2. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

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  3. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : (1...

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  4. If 1,a1,a2,a3,…,a(n-1) are the nth roots of unity then prove that : 1+...

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  5. If alpha is an n^(th) roots of unity, then 1+2alpha+3alpha^(2)+……..+n...

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  6. If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + ...

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  7. sum(p=1)^pi(3p+2)[sum(q=1)^10sin(2qpi)/11-icos(2qpi)/11]^p

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  8. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

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  9. If alpha ia ROOT OF x^2+x+1= 0 then show that alpha is also a root of...

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  10. If p,q,r are three consecutive integers ge3, prove that x^p+x^q+x^r is...

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  11. If n is n odd integer that is greater than or equal to 3 but not la ul...

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  12. If z^2(bar omega)^4=1 where omega is a nonreal complex cube root of 1 ...

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  13. Find z satisfying |z-5i|le3 such that amp z is the minimum.

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  14. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

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  15. Find the complex number Z, the greatest in absolute value which satisf...

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  16. Complex number z1, z2 and z3 in AP

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  17. if |(1-iz)/(z-i)|=1 prove that the locus of the variable point z in th...

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  18. The equation barbz+bbarz=c, where b is a non-zero complex constant and...

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  19. Let A(z1) and (z2) represent two complex numbers on the complex plan...

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  20. Find the area of the triangle whose vertices in the Argand plane are i...

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