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The real value of theta for which the ex...

The real value of `theta` for which the expression `(1 -isin theta)/(1 + 2 isin theta)` is a real number is

A

`theta = npi`

B

`theta = npi//2`

C

`theta = npi//3`

D

`theta = npi//4`

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The correct Answer is:
A
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AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If (x + 3i)/(2 + iy) = 1 - i then the value of (5x - 7y)^(2) =

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  2. If x + iy = (1)/((1 + cos theta + isin theta)) then sin^(-1) x =

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  3. The real value of theta for which the expression (1 -isin theta)/(1 + ...

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  4. Find the values of the following : ( sqrt3/2 + i/2)^(5) - ( sqrt3/...

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  5. If x = (-5 + isqrt3)/(2) then (x^(2) + 5x)^(2) + x ( x+ 5) =

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  6. If z = 3- 5i then z^(2) - 10z + 30=

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  7. If theta is real then the modulus of (1)/(1 + cos theta + isin theta) ...

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  8. If (x + iy)^((1)/(3)) = 5+ 3i , then 3x + 5y =

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  9. If alpha is a non-real root of x^(7) = 1 then alpha(1 + alpha) (1 + al...

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  10. Express (3- 2i)/(5 + 4i) + (3 + 2i)/(5 - 4i) in the form of a + ib

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  11. The conjugate of (2 + 3i)/(1 + 2i) is

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  12. If (2 - i)/((1 - 2i)^(2)) and (-(x + 11i))/(25) are conjugate complex ...

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  13. The modulus of ((3 + i) (2 - i))/(1 +i) is

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  14. If x -iy = sqrt([(a - ib)/(c-id)]) , then (x^(2) + y^(2))^(2) =

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  15. If m1,m2,m3 and m4 respectively denote the moduli of the complex numbe...

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  16. The mod-amplitude form of -sqrt3 - i

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  17. The mod-amplitude form of sin theta + icos theta is

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  18. If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos...

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  19. If (pi)/(5) and (pi)/(3) are respectively the arguments of barz(1) and...

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  20. If Arg (3z-2i) = pi//2 then the locus of z = x +iy is

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