Question

compute the product (-3,5)(2,-4) in Z4*Z11​

Answer 1

looks like OP is good to go, but just for completeness:

Suppose R1 and R2 are rings. Then the direct product of two rings, R1×R2 is defined as follows:

(a,b)∈R1×R2⟺a∈R1 and b∈R2. And further, for any (a,b) and (c,d)∈R1×R2:

(a,b)+(c,d)=(a+c,b+d)

(a,b)⋅(c,d)=(a⋅c,b⋅d)

Where a+c and a⋅c are carried out as they would be in R1, and likewise for b and d in R2.