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

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

A

a.1

B

b.-1

C

c.i

D

d.-i

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If theta=(pi)/(6) then the 10^(th) term of the series 1+(cos thet...

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

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

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

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

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

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  7. (1+cos theta+i sin theta)^(10)+(1+cos theta-i sin theta)^(10)=

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

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

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  10. (1+i sqrt(3))^(5)+(1-i sqrt(3))^(5)=

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

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

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

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

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

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

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  17. sqrt(i)+sqrt((-i)) equals :

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  18. If the fourth roots of unity are z(1), z(2), z(3), z(4) then z(1)^(2)+...

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  19. If alpha and beta are non real cube roots of unity then alpha beta+alp...

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  20. The value of ((-1+i sqrt(3))/(2))^(26)+((-1-i sqrt(3))/(2))^(26) is

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