Find the values of x and y, where x,y ∈R
2x + y + (x−y)i = 4 + i
Real part: 2x + y = 4
Imaginary part: x - y = 1
Add these term by term: 3x = 5 so x = 5/3
Put this back into the second equation: 5/3 - y = 1 so y = 5/3 - 1 or y = 2/3
x = (1/5+(2 i)/5) ((1+i) y+(1-4 i))
y = (3/2+(5 i)/2)-(1/2+(3 i)/2) x
