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Find the theta such that (3+2i sin theta...

Find the `theta` such that `(3+2i sin theta)/(1-2 isin theta)` is
(a) real
(b) purely imaginary

A

` n pi `

B

` ( n pi)/( 2)`

C

` n pi pm ( pi)/( 3)`

D

` 2 n pi pm (pi)/( 4)`

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The correct Answer is:
A, C
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If x^(2) - 2 x cos theta + 1 = 0 " then " x^(2 n) - 2 x ^(n) cos n th...

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  2. The following in the form A + i B ( cos 2 theta + i sin 2 theta )^(-...

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  3. If x = cos theta + i sin theta , y = cos phi + i sin phi z = cos Ps...

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  4. If a = cos alpha + i sin alpha , b = cos beta + i sin beta , " then ...

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  5. If cos A + cos B + cos C = 0, sin A + sin B + sin C = 0 and A + B +...

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  6. If cos A + cos B + cos C = 0 = sin A + sin B + sin C , then

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  7. The general value of x which satisfies the equation ( cos x + i sin ...

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  8. Find the theta such that (3+2i sin theta)/(1-2 isin theta) is (a) re...

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  9. If ( tan theta - i [ sin ( theta // 2) + cos ( theta // 2) ])/( 1 + 2...

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  10. Let f(p) ( beta) = ( cos "" (beta)/( p^(2)) + i sin "" (beta)/( p^(2)...

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  11. The continued product of the four values of [ cos (pi/ 3) + i sin (...

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  12. If a = cos alpha + i sin alpha, b = cos beta + i sin beta , " then " ...

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  13. If alpha , beta be the roots of the the equation x^(2) - 2 x + 2 =...

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  14. The complex number z has argZ = theta ,0 lt theta lt (pi)/(2) and sat...

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  15. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

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  16. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

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  17. 1 + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega...

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  18. 1 + i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega...

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  19. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1 + omega ...

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  20. 1+ i = sqrt(2) ( cos "" (pi)/( 4) + i sin "" (pi)/( 4)) 1+ omega ...

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