Question 725092
(x+i)(3-iy)= 1+13i

(3x+y)+(3-xy)i=1+13i


(1) 3x+y=1, 
(2) 3-xy=13

(2) 3-xy=13,  xy=-10,  y=-10/x


(1) 3x+y=1, 3x+(-10/x)=1, 3x^2-x-10=0, x=2, x=-5/3


then 

(x,y)=(2,-5)

or


(x,y)=(-5/3, 6)