Assume:j=√-1 and jx/(1+jy)=(3x+j4)/(x+3y); cross multiply:
jx(x+3y)=(3x+j4)(1+jy)=3x+3jxy+j4-4y,
jx2+3jxy=3x+3jxy+j4-4y,
jx2=3x+j4-4y; separate real and imaginary components:
Imaginary:
x2=4, x=±2;
Real:
3x-4y=0, 3x=4y, y=¾x, so y=±3/2.
SOLUTION: (2,3/2) or (-2,-3/2) for (x,y).