Solution:

             Given,

                    (x+iy)³= u + iv

                  or,  x³ + 3x²yi + 3xi²y² + i³y³= u + iv

                   or,  x³ – 3xy² + 3x²iy – iy³= u + iv

                     or, x(x² – 3y²) + y(3x² – y²)i= u+iv

Comparing Corresponding Terms,

        u = x(x² – 3y²)                   and              v = y(3x² – y²)

    Now,

       LHS = u/x + v/y

                 = (x(x² – 3y²))/x + (y(3x² – y²))/y

                   = (x² – 3y²) + (3x² – y²)

                     = 4x² – 4y²

                                  = 4(x² – y²)

                        = RHS

                                                                      Proved.......