Answer:
see explanation
Step-by-step explanation:
Expand the left side and equate to like terms on the right side
(2 - 3i)(x + yi)
= 2x + 2iy - 3ix - 3yi² ← using i² = - 1, then
= 2x + 2iy - 3ix + 3y → compare with 4 + i
2x + 3y = 4 → (1)
- 3x + 2y = 1 → (2)
Multiply (1) by 3 and (2) by 2
6x + 9y = 12 → (3)
- 6x + 4y = 2 → (4)
Add (3) and (4) term by term to eliminate term in x
13y = 14 ( divide both sides by 13 )
y = [tex]\frac{14}{13}[/tex]
Substitute this value into (1) and solve for x
2x + [tex]\frac{42}{13}[/tex] = [tex]\frac{52}{13}[/tex]
Subtract [tex]\frac{42}{13}[/tex] from both sides
2x = [tex]\frac{10}{13}[/tex] ← divide both sides by 2
x = [tex]\frac{5}{13}[/tex]
Hence x = [tex]\frac{5}{13}[/tex] and y = [tex]\frac{14}{13}[/tex]
