Sum of Complex Numbers

Algebra Level 3

Let f(A,B)=A+BiABif(A,B)=\frac{A+Bi}{A-Bi}, where AA and BB are non-zero real numbers. If CC and DD are real numbers such that f(2,1)+f(4,2)+f(6,3)+f(8,4)+f(10,5)=C+Di,f(2,1)+f(4,2)+f(6,3)+f(8,4)+f(10,5)=C+Di, what is the value of C+D?C + D?

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