Thanks a lot for your suggestion. But I have already applied another trick (multiplying and dividing expr1 by complex conjugate of denominator of expr1 ) and I also did as you said ( there was a little error in your suggestion which I corrected); but both ways give me some error in final expression (precision and accuracy related, since there are very high negative powers). For example,

ComplexExpand[Conjugate[Denominator[expr1]]] * Denominator[expr1] 

should be real but it is not so. In the same way mathematica is not performing truthfully for

 ComplexExpand[Conjugate[Denominator[expr1]]] * Numerator[expr1] 

Command Chop is not effective here since I expect high negative exponents in my desired expression.

Thanks for the help. My goal is first to solve two parts (real and imaginary) for Rdot. Later I want to extract coefficient of theta (with specific exponent) from Rdot. Then I expect to get a relation between Rdot and theta in terms of another paramters followed by continuation method to investigate the trend among paramters.