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(cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(c...

`(cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(11//2)`

A

`-1`

B

1

C

0

D

2

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

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  2. The modulus of sqrt2i-sqrt(-2i) is

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  3. (cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(...

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  4. If n is a multiple of 3 then omega^(n) + omega^(2n) =

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  5. (1+omega-omega^(2))(1-omega+omega^(2))

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  6. (2+omega^(2)+omega^(4))^(5)

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  7. (3+5omega+3omega^(2))^(6)

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  8. (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^...

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  9. (1+omega)(1+omega^(2))(1+omega^4)(1+omega^(5))..........2n factors =

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  10. (1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+...

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  11. (1-omega+omega^(2))^(7)+(1+omega-omega^(2))^(7)

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  12. (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

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  13. If omega is a complex cube root of unity, then 225+(3omega+8omega^(2))...

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  14. If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-...

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  15. (a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

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  16. (a+2b)^(2)+(aomega+2bomega^(2))^(2)+(aomega^(2)+2bomega)^(2)

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  17. If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3...

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  18. If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then xyz

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  19. If a, b are real and x=a+b,y=aomega^(2)+bomega,z=aomega+bomega^(2)" th...

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  20. (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-om...

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