If 2z+3-2i = (2z-i)/2 find z.

2z+3-2i = (2z-i)/2 . To find
z.

First we simplify the right side as z-(1/2) and then we
move the z's to left and numbers to the right as below:

2z
+3-2i  = z- (1/2)i.

Subtract z from both
sides:

2z-z + 3-2i =
-(1/2)i.

z+3-2i =
-(1/2)i.

Subtract 3-2i from both
side:

z = -(1/2)i-(3-2i).

We
add the like terms on the right.

z =  -3 - 1/2i
+2i.

z = -3 +(2-1/2)i.

z = -3
+(3/2)i.