Solve for x and y which are both real numbers? Given that 4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i

Answer

4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i

Separate the ‘real’ and ‘complex’ part as follows:

(4x – 3y -12) + (3y + 12)i = ( 9-2x ) + ( 1 -2y –2x )i

“equate them” [ complex coefficients with complex coefficients and real ] :

For the “real” we get,
(4x – 3y -12) = ( 9-2x )
6x = 3y + 21
2x = y + 7
y = 2x – 7 ….(1)

For the “complex part”, we get
( 1 -2y –2x ) = (3y + 12)
5y = -11 -2x …(2)

Put (1) in (2),
5( 2x – 7 ) = -11 -2x
10x – 35 = -11 -2x
12x = 35 – 11
12x = 24
x=2

and so y = 2x -7 = 2(2) – 7 = -3

Hence,

(x,y) =(2, -3)