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Find real theta such that (3+2i sin th...

Find real `theta` such that
`(3+2i sin theta)/(1-2i sin theta)` is purely real.

A

`pi`

B

`(pi)/(2)`

C

`(pi)/(3)`

D

`(pi)/(4)`

Text Solution

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The correct Answer is:
A
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KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-TEXTBOOK BASED MCQS
  1. Find real theta such that (3+2i sin theta)/(1-2i sin theta) is purel...

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  2. The polar form of ((i)^(25))^(3) is....

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  3. If (1+i)(1+2i)(1+3i)....(1+ni)=a+ib then 2xx5xx10xx....xx(1+n^(2))=...

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  4. (sqrt(-2))(sqrt(-3))=.....

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  5. If z=(1+2i)/(1-(1-i)^(2)) then arg (z).....

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  6. If z=(1)/((2+3i)^(2)) then |z|=...

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  7. If z=(1)/(1-cos theta- isintheta) then Re(z)=....

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  8. (1+i)^(4)+(1-i)^(4) = ........ .

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  9. If one complex number is in third quadrent then its conjugate complex ...

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  10. In Argand figure complex number (1+2i)/(1-i) lies in ......... quadren...

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  11. If |z-1|^(2)=|z|^(2)+1 then in the grand plane, z lines an.....

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  12. If |z+4|le3 then the maximum value fo |z+1| is....

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  13. Inverse of (3+4i)/(4-5i)

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  14. If (sqrt(8)+i)^(50)=3^(49)(a+ib) then a^(2)+b^(2)=....

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  15. If arg (z) lt 0 then arg(-z)-arg(z)=.....

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  16. If |(z-2)/(z-3)|=2 express a circle, then its radius is ......

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  17. If the conjugate complex number of (x+yi)(1-2i) is 1+i then ......

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  18. If z=cos((pi)/(3))-isin((pi)/(3)) then z^(2)-z+1=....

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  19. n is any integer then arg(((sqrt(3)+i)^(4n+1))/((1-sqrt(3)i)^(4n)))=.....

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  20. If (2z(1))/(3z(2)) is pure imaginarny then |(z(1)-z(2))/(z(1)+z(2))|=....

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