Find x and y if (x+ iy) (2 - 3i) = 4 + i

1.	Find x and y if (x+ iy) (2 - 3i) = 4 + i
Answer» Given, (x + iy) (2 − 3i) = 4 + i ⟹ (2x + 3y) + i(−3x + 2y) = 4 + i ⟹ 2x + 3y = 4 and − 3x + 2y = 1 On solving, we get, x = \(\frac{5}{13}\) and y = \(\frac{14}{13}\)

Answer»

Given, (x + iy) (2 − 3i) = 4 + i

⟹ (2x + 3y) + i(−3x + 2y) = 4 + i

⟹ 2x + 3y = 4 and − 3x + 2y = 1

On solving, we get,

x = \(\frac{5}{13}\) and y = \(\frac{14}{13}\)

Discussion