InterviewSolution
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InterviewSolution
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Find real q such that `(3+2isintheta)/(1-2isintheta)`is purelyreal. |
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Answer» We have `((3+2i sin theta)/(1-2i sin theta))=((3+2i sin theta))/((1-2i sin theta))xx((1+2i sin theta))/((1+2i sin theta))` `=((3+2i sin theta)(1+2i sin theta))/((1-4i^(2) sin^(2)theta))` `=((3-4sin^(2)theta)+i(6sin theta+2sin theta))/((1+4 sin^(2)theta))` `=((3-4sin^(2)theta)+i(8sin theta))/((1+4 sin^(2)theta))` Now, `((3+2i sin theta)/(1-2i sin theta))` will be purely real only when `(8 sin theta)/((1+4sin^(2) theta))=0`. This happens only when `8 sin theta = 0 iff sin theta = 0 iff theta = n pi, n in N`. Hence, the required value of `theta` is `n pi`, where n `in` N. |
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