Algebra 2 honors help?

Question

what is (3+2i)(4-3i)/((3+2i)+(4-3i)) 

i'm thinking it is 127+11i/50 but im not sure how i got that answer..

Thank You!

Answer 1

(3 + 2i)(4 - 3i) / (3 + 2i) + (4 - 3i) = (12 - 9i + 8i - 6i^2 ) / (7 - i)

substitute  of  i^2 = -1

                                                        =(12 - i + 6) / (7 - i)

                                                       =(18 - i) / (7 - i)

Multiply numerator and denominator by conjugate of  7 - i

                                                      =(18 - i)(7 + i) / (7 - i)(7 + i)

                                                      =(126 + 18i - 7i - i^2) / (49 - i^2)

                                                     =(126 + 11i -(-1)) / (49 -(-1))

                                                    =(127 + 11i) / 50.