What are x and y if (3x+2iy)-(y-2ix)-2x=3-2i ?

We have (3x+2iy)-(y-2ix)-2x=3-2i and we need to find x and
y.

(3x + 2iy) -(y - 2ix) - 2x = 3 -
2i

=> 3x + 2iy - y + 2ix - 2x = 3 -
2i

=> x - y + 2i(x + y) = 3 -
2i

equate the real and imaginary
coefficients

x - y = 3 and x + y =
-1

adding the two

2x =
2

=> x = 1

y =
-2

The solution is x = 1 and y =
-2