Evaluate the complex number into real and imaginary parts ii

Solution

From indices we know that i=i12
i12=[cosπ2+isinπ2]12=cosπ4+isinπ4=12+i12.
 


Therefore, 



=eπ42.eiπ42=eπ42.[cosπ42+isinπ42]
Therefore, the
Real part =eπ42cosπ42
Imaginary part =eπ42sinπ42