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I hope there is no direct representation of complex numbers in 8051.
So in a way, I assume you have two set of numbers. Real part of No1, Imaginary part of No1, Real part of No2, Imaginary part of No2. In this case, your addition is simple addition of real parts and imaginary parts and store in same way the inputs are stored.
The assembly code for above is
complex addition is no thing more than a normal addtion. the real and imaginary parts are added individually the have no link like overfolw or anything else.
you have to get real and imaginary part of both numbers and then add individually.
if your complex number is in polar form then it will be a bit diffrent.