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If `1,alpha_1,alpha_2, ,alpha_(n-1)` are the `n t h` roots of unity, prove that `(1-alpha_1)(1-alpha_2)(1-alpha_(n-1))=ndot` Deduce that `sinpi/nsin(2pi)/n sin((n-1)pi)/n=n/(2^(n-1))`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Evaluate x=sqrt(6+sqrt(6+sqrt(6+oodot)))

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  2. If a complex number z satisfies |2z+10+10 i|lt=5sqrt(3)-5, then the le...

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  3. If 1,alpha1,alpha2, ,alpha(n-1) are the n t h roots of unity, prove t...

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  4. If n >1 , show that the roots of the equation z^n=(z+1)^n are collinea...

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  5. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  6. If |z2+i z1|=|z1|+|z2| and|z1|=3 and |z2|=4, then the area of triangl...

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  7. What is the locus of w if w=3/za n d|z-1|=1?

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  8. If z is complex number, then the locus of z satisfying the condition...

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  9. Find the remainder when x^3+4x^2-7x+6 is divided by x-1.

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  10. What is the locus of z if ||z-cos^(-1)cos12|-|z-sin^(-1)s in 12||=8(pi...

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  11. Use the factor theorem to find the value of k for which (a+2b),w h e ...

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  12. If z is a complex number lying in the fourth quadrant of Argand plane ...

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  13. If z=(lambda+3)+isqrt(5-lambda^2) then the locus of Z is

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  14. Let z be a complex number having the argument theta ,0 < theta < pi/2,...

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  15. Given that x^2+x-6 is a factor of 2x^4+x^3-ax^2+b x+a+b-1, find the va...

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  16. If z is any complex number such that |3z-2|+|3z+2|=4 , then identify t...

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  17. If p ,q ,r are positive and are in A.P., the roots of quadratic equat...

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  18. A(z1),B(z2),C(z3) are the vertices of the triangle A B C (in anticlock...

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  19. If |z^2-1|=|z|^2+1, then z lies on (a) The Real axis (b)The imaginary...

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  20. A(z1),B(z2),C(z3) are the vertices of he triangle A B C (in anticlockw...

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