Theorem 4.6.  Let  [Graphics:Images/ComplexSequenceSeriesMod_gr_253.gif]  be convergent series, and let  c  be a complex number.  Then  

            [Graphics:Images/ComplexSequenceSeriesMod_gr_254.gif]  
        and  
            [Graphics:Images/ComplexSequenceSeriesMod_gr_255.gif].  

Proof.

Proof of Theorem 4.6 is left as an exercise in the book.

Complex Analysis for Mathematics and Engineering