Question: Plotting Real and Imaginary Parts?

I have this function:

Eig1 := proc (R) options operator, arrow; (1/9*(-27*deltaE^3*R^9-10*M^6+3*sqrt(-189*deltaE^4*R^12*M^4-147*deltaE^2*R^6*M^8-27*M^12+60*deltaE^3*R^9*M^6))^(1/3)-(-deltaE^2*R^6-7/9*M^4)/(-27*deltaE^3*R^9-10*M^6+3*sqrt(-189*deltaE^4*R^12*M^4-147*deltaE^2*R^6*M^8-27*M^12+60*deltaE^3*R^9*M^6))^(1/3)+2/3*deltaE*R^3+2/9*M^2)/R^3 end proc

where:

> deltaE := 0.355 , and

M := sqrt(540000.0000)

All I want to do is plot: Re(Eig1) vs R  , and Im(Eig1) vs R , but it seams like everything I try doesn't work. 

I can't even evaluate the limit of Eig1 as R goes to infinity.  I use limit(Eig1,R=infinity) and nothing happens.

  Likewise, if I try limit(Re(Eig1) , R=infinity) , it doesn't work either.

Can someone please help?  Thank you so much.  The limits aren't as important as the plotting since I can deduce the limits from the plots.