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Prove the following (a + b omega + c o...

Prove the following
`(a + b omega + c omega^(2))/(b + c omega + a omega^(2))= omega`

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Prove the following (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + c omega^(2))/(b + c omega + a omega^(2)) = -1

Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (1 - omega- omega^(2))= 8

Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4)) (1- omega^(4) + omega^(8)) …. to 2n factors = 2^(2n) where , ω is the cube root of unity.

Prove the following (1+ omega) (1+ omega^(2)) (1 + omega^(4)) (1 + omega^(8)) ….to 2n factors = 1

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If 1, omega, omega^(2) are cube roots of unity, prove that (x + y)^(2) + (x omega + y omega^(2))^(2) + (x omega^(2) + y omega)^(2)= 6xy

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

Given that 1, omega, omega^(2) are cube roots of unity. Show that (1- omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5)= 32

Prove that the lines ax+by + c = 0, bx+ cy + a = 0 and cx+ay+b=0 are concurrent if a+b+c = 0 or a+b omega + c omega^(2) + c omega = 0 where omega is a complex cube root of unity .

If omega and omega^(2) are cube roots of unity, prove that (2- omega + 2omega^(2)) (2 + 2omega- omega^(2))= 9

ICSE-COMPLEX NUMBERS-Exercise (F )
  1. If omega is a cube root of unity, then omega^(3)= ……

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  2. If 1, omega, omega^(2) are three cube roots of unity, prove that (1...

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  3. If 1, omega, omega^(2) are three cube roots of unity, prove that (1...

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  4. If 1, omega, omega^(2) are three cube roots of unity, prove that (1...

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  5. If 1, omega, omega^(2) are three cube roots of unity, prove that (1...

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  6. If 1, omega, omega^(2) are three cube roots of unity, prove that (1...

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  7. If 1, omega, omega^(2) are three cube roots of unity, prove that (...

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  8. If 1, omega, omega^(2) are three cube roots of unity, prove that (3...

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  9. If 1, omega, omega^(2) are three cube roots of unity, prove that om...

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  10. Prove that ((-1 + isqrt3)/(2))^(n) + ((-1-isqrt3)/(2))^(n) is equal to...

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  11. If 1, omega, omega^(2) are the cube roots of unity, prove that omega^(...

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  12. Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (...

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  13. Prove the following (1+ omega) (1+ omega^(2)) (1 + omega^(4)) (1 + ...

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  14. Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4...

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  15. Prove the following (a + b omega + c omega^(2))/(b + c omega + a ome...

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  16. Prove the following (a + b omega + c omega^(2))/(c + a omega + b ome...

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  17. If omega is a cube root of unity and n is a positive integer which is ...

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  18. Show that (x + omega y + omega^(2)z) (x + omega^(2)y + omega z) = x^(2...

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  19. Show that x^(3) +y^(3) = (x + y) (omega x + omega^(2)y) (omega^(2)x +...

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  20. If 1, omega, omega^(2) are cube roots of unity, prove that 1, omega, o...

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