Find real `theta` such that `(3+2isintheta)/(1-2isintheta)`is purely r – InterviewSolution

InterviewSolution

1.	Find real `theta` such that `(3+2isintheta)/(1-2isintheta)`is purely real.
Answer» `(3+2isintheta)/(1-2isintheta) = (3+2isintheta)/(1-2isintheta)**(1+2isintheta)/(1+2isintheta)` `=((3+2isintheta)(1+2isintheta))/(1-4i^2sin^2theta))` `=(3+6isintheta+2isintheta+4i^2sin^2theta)/(1+4sin^2theta)` `=(3-4sin^2theta)/(1+4sin^2theta)+(8sintheta)/(1+4sin^2theta)i` For this number to be real, imaginary part should be `0`. So, `(8sintheta)/(1+4sin^2theta) =0` `=>sintheta =0=>theta = npi` So, when `theta = npi`, given number will be real.

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