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Find the real values of theta , such tha...

Find the real values of `theta` , such that `(3 + 2i sin theta)/(1 - 2i sin theta)` is purely
Imaginary

A

`n pi , n in Z `

B

`n pi pm (pi)/(2) , n in Z `

C

`n pi pm (pi)/(3) , n in Z `

D

`n pi pm (pi)/(6) , n in Z `

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If (1 + cos theta + isin theta) (1 + cos 2 theta + isin 2theta) = x + ...

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  2. If (x + iy)^((1)/(3)) = a+ ib , then ((x)/(a)) + ((y)/(b)) =

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  3. Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i s...

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  4. If (sin(x //2) + cos (x//2) + itan x )/(1 + 2isin (x //2)) is real th...

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  5. If |{:(6i , -3i , 1) , (4 , 3i , -1) , (20 , 3 , i):}| = x +iy show t...

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  6. If (a+ ib)^(5) = alpha + ibeta then (b + ia)^(5) =

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  7. If x=-5+4i then x^4+9x^3+35x^2-x+4=

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  8. If the point z = (1+i) (1+2i)(1+3i)…(1+10i) lies on a circle with cent...

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  9. If (2 + 3 isin theta)/(1- 2isin theta) is purely imaginary , then cos^...

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  10. If the first term and common ratio of a G.P are both (1//2) (sqrt(3)+i...

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  11. If (1 + cos theta - isin theta) ( 1+ cos 2 theta + isin 2 theta) = x +...

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  12. If (5z2)/(7z1) is purely imaginary , then |(2z1+3z2)/(2z1-3z2)|=

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  13. If alpha and betaare different complex numbers with |beta| =1 , then |...

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  14. If z(1) , z(2) are two complex numbers satisfying |(z(1) - 3z(2))/(3 -...

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  15. If |z-4/z|=2 , then the maximum value |z| is equal to

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  16. The minimum value of |z-1|+ |z-5| is

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  17. If |z + 2- i| = 5 then the maximum value of |3z- 9 - 7i| is

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  18. The minimum value of |z - 1| + | z- 2| + |z -3| + |z - 4|+ |z - 5| i...

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  19. If |z+ 4| le 3 then the maximum value of |z + 1|

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  20. If |z(1)| = |z(2)| = |z(3)| = … |z(n)| = 1 , then |z(1) + z(2) + z(3) ...

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