@Carl Love Thank you Carl, my maple version is 18 and it's the newst version as far as I know. The problem was some predefined variables causing trouble in the output. I got the right results as soon as I typed the restart command.

@Kitonum Thank you very much the problem is solved.

@Kitonum 

Dear Kitonum, could you type here what maple gives for a and b as the answer in your version of maple?

@Carl Love 

Dear Carl I do so, but maple gives an expression like this:

-Re(((I*Eml-Ef+Ems)*Zeta*phi+I*Eml+Zeta*Ef+Ems)*(Ems+I*Eml)/((I*Eml-Ef+Ems)*phi-I*Eml-Zeta*Ef-Ems)):

unfortanately some imaginary terms still exist in the above expression.