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((1+cos""(pi)/(8)-isin""(pi)/(8))/(1+cos...

`((1+cos""(pi)/(8)-isin""(pi)/(8))/(1+cos""(pi)/(8)+isin""(pi)/(8)))^(8)`

A

1

B

`-1`

C

2

D

`1//2`

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DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. ((1)/(2)+sqrt(3)/(2)i)^(6)

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  2. If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinn...

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  3. ((1+cos""(pi)/(8)-isin""(pi)/(8))/(1+cos""(pi)/(8)+isin""(pi)/(8)))^(8...

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  4. [(1+sin(pi//8)+icos(pi//8))/(1+sin(pi//8)-icospi//8)]^(-8//3)

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  5. ((sinpi//8+icospi//8)/(sinpi//8-icospi//8))^(8)

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  6. ((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)

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  7. If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n)...

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  8. (1+i)^(5)+(1-i)^(5)

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  9. (sqrt3+i)^(7)+(sqrt3-i)^(7)

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  10. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

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  11. If n is a positive niteger, then (sqrt3+i)^(n)+(sqrt3-i)^(n)

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  12. If n is a positive integer and (1+isqrt3)^(n)+(1-isqrt3)^(n)=2^(n+1)co...

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  13. If n is an integer which leaves remainder one when divided by three, t...

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  14. ((-1+isqrt3)/(2))^(3n)+((-1-isqrt3)/(2))^(3n)

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  15. (1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)

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  16. (costheta+isintheta)^(10)+(costheta-isintheta)^(10)

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  17. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

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  18. [(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(...

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  19. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

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  20. A value of n such that ((sqrt3)/(2)+(i)/(2))^(n)=1 is

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