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Let z = (1 + 2 icos theta)/(2 - i sin th...

Let `z = (1 + 2 icos theta)/(2 - i sin theta)` and set S consist of values of `theta in (0, 2pi)` such that `z = barz` then number of elements in set S is :

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The correct Answer is:
2
`z = (1 + 2 icos theta)/(2 - I sin theta) barz = implies z` is purely real
`z = ((1 + 2icos theta)(2 + isin theta))/(4 + sin^2 theta)`
`lim(z) = (4 cos theta + sin theta)/(4 + sin^2 theta) = 0 implies tan theta = - 4`
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