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If z^(2) + z + 1 = 0, where z is a compl...

If `z^(2) + z + 1 = 0`, where z is a complex number , prove that
` ( z + 1/z)^(2) + ( z^(2) + 1/z^(2)) + (z^(3) + 1/z^(3))^(2) + (z^(4) + 1/z^(4))^(2) + (z^(5) + 1/z^(5)) ^(2) + ( z^(6) + 1/z^(6)) = 12 `.

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DE MOIVRE'S THEOREM-EXERCISE - 2 (b)
  1. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  2. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  3. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  4. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  5. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  6. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  7. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

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  8. Solve the following equations. x^(4) - 1 = 0

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  9. Solve the following equations. x^(5) + 1 = 0

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  10. Solve the following equations. x^(9) - x^(5) + x^(4) - 1 = 0

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  11. Solve the following equations. x^(4) + 1 = 0

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  12. Find the number of 15^(th)roots of unity, which are also 25^(th) roots...

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  13. If the cube roots of unity are 1 , omega , omega^(2), then find the r...

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  14. Find the product of all the values of (1 + i)^(4//5).

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  15. If z^(2) + z + 1 = 0, where z is a complex number , prove that ( z...

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  16. If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity,...

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  17. Prove the sum of 99t^(th) powers of the roots of the equation x^7-1 = ...

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  18. If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^...

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  19. Show that one value of ((1 + sin . pi/8 + i cos . pi/8)/(1 + sin . p...

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  20. Solve (x - 1)^n =x^n, where n is a positive integer.

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