if A+iB = (a.+ib.) (a,+ib,), prove (a.^2+b.^2) (a,^2 +b,^2 ) = (A^2 + B^2)

a. & b. is suppose to be subcript 1 and a, & b, is suppose to be subscript 2.

i dont see any short way of proving this, i have tried squaring A+iB and re-arranging to prove (A^2 + B^2) but hit a dead end.

any suggestions on how to attemp?