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

Given, `z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1),` 'n' a positive integer , find the equation whose roots are, `alpha=z+z^3+……..+z^(2n-1) & beta=z^2+z^4+……..+z^(2n)` .

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The correct Answer is:
`z^2=k,y+(sin^2ntheta)/(sin^2theta) ," where " theta=(2pi)/(2n+1)`
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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
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  3. Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1), 'n' a positive integer ...

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

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

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

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

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

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

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  19. 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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  20. (1+w)^7=A+Bw where w is the imaginary cube root of of a unity and A, B...

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