Find the real values x and y given that 12+3i/x-iy=-1-i

Answer 1

assuming you mean:
(12+3i)/(x-iy)=-1-i , those brackets are critical!
(x - iy)(-1 - i) = 12 + 3i
-x - xi + iy + i^2 y = 12 + 3i
-x - xi + iy - y = 12 + 3i

matching up real and complex
-x - y = 12 and
-xi + iy = 3i or x - y = -3

add the two bold equations:
-2y = 9
y = -9/2
then x = -15/2