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

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

A

1+i

B

1-i

C

1

D

-1

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. ((cos theta+i sin theta)/(sin theta+i cos theta))^(4)=

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  2. ((sin (pi/8)+i cos (pi/8))/(sin (pi/8)-i cos (pi/8)))^(8)=

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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. The value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqr...

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  5. If theta=(pi)/(6) then the 10^(th) term of the series 1+(cos thet...

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  6. If 2 cos theta=x+(1)/(x) and 2 cos phi=y+(1)/(y) then the value of ...

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  7. The value of (sin (pi/3)+i cos (pi/3))^(3) is

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  8. (sin theta+i cos theta)^(9)=

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  9. (sin theta+i cos theta)^(9)=

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  10. If n is an integer and z=cos theta+i sin theta, then (z^(2 n)-1)/(z^(...

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  11. (1+cos theta+i sin theta)^(10)+(1+cos theta-i sin theta)^(10)=

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  12. The value of (a+i b)^(m / n)+(a-i b)^(m / n) is equal to

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  13. (sqrt(3)+i)^(6)+(sqrt(3)-i)^(6)=

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  14. (1+i sqrt(3))^(5)+(1-i sqrt(3))^(5)=

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  15. If one of the values of (cos theta+i sin theta)^(t / 3) is cos (theta)...

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  16. The product of the values of (cos ((pi)/(3))+i sin( (pi)/(3)))^(3 / 4)...

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  17. The continued product of the cube roots of 3+sqrt(3) i is

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  18. The continued product of the fourth roots of -1+i sqrt(3) is

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  19. If one of the square roots of sqrt(3)-i is sqrt(2) cis (-(pi)/(12)) th...

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  20. If one of the cube roots of i is cis (pi)/(6) the other two roots are

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