Q. 64.8( 10 Votes )

Find the real values of θ for which is purely real.

Answer :

Since is purely real

Firstly, we need to solve the given equation and then take the imaginary part as 0



We rationalize the above by multiply and divide by the conjugate of (1 -2i cos θ)




We know that,


(a – b)(a + b) = (a2 – b2)




[ i2 = -1]




Since is purely real [given]


Hence, imaginary part is equal to 0


i.e.


3 cos θ = 0 × (1 + 4 cos2θ)


3 cos θ = 0


cos θ = 0


cos θ = cos 0


Since, cos θ = cos y


Then where n Є Z


Putting y = 0



where n Є Z


Hence, for is purely real.


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