InterviewSolution
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InterviewSolution
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A value of `theta` for which `(2+3isintheta)/(1-2isintheta)`purely imaginary, is :(1) `pi/3`(2) `pi/6`(3) `sin^(-1)((sqrt(3))/4)`(4) `sin^(-1)(1/(sqrt(3)))` |
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Answer» `(2+3isintheta)/(1-2isintheta) ** (1+2isintheta)/(1+2isintheta)` `=(2+4isintheta+3isintheta+6i^2sin^2theta)/(1-4i^2sin^2theta)` `=(2-6sin^2theta+7isintheta)/(1+4sin^2theta)` `=(2-6sin^2theta)/(1+4sin^2theta) +i(7sintheta)/(1+4sin^2theta)` For this number to be purely imaginary, `(2-6sin^2theta)/(1+4sin^2theta) = 0` `=> 2 - 6sin^2theta = 0` `=>sin^2theta = 1/3` `=> sintheta = 1/3` `=> theta = sin^-1(1/sqrt3)` So, option (4) is the correct option. |
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