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If 1//x+x=2costheta , then prove that x^...

If `1//x+x=2costheta` , then prove that `x^n+1//x^n=2cosnthetadot`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the root of equation 2x^2+10 x + 20=0.

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  2. Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The max...

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  3. If 1//x+x=2costheta , then prove that x^n+1//x^n=2cosnthetadot

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  4. If a x^2+b x+c=0 and b x^2+c x+a=0 have a common root and a, b, and c ...

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  5. Find the roots of the equation 2x^2 - x + 1/8 = 0

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  6. If |z +2 - i|=5 then the maximum value of |3z+9-7i| is K, then find k

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  7. If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in ...

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  8. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

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  9. The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and a...

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  10. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

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  11. Express 1/(1-costheta+2isintheta) in the form x+i y .

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  12. a ,b ,c are three complex numbers on the unit circle |z|=1, such that ...

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  13. If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the eq...

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  14. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

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  15. If |z1|=15 and |z2-3-4i|=5,t h e n

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  16. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

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  17. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)

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  18. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

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  19. If alpha,beta are the roots of the equation a x^2+b x+c=0, then find t...

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  20. If (pi)/2 < alpha < (3pi)/2 then the modulus argument of (1+cos 2alpha...

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