Question

find the value of x and y if (x+iy)(5+3i)=3-4i

Answer 1

Answer:

(x + iy)(2–3i) = 4 + i

⇒(2x + 3y) + i(2y– 3x) = 4 + i

⇒2x + 3y = 4 and 2y – 3x = 1

x = 5/13 and y = 14/13

Answer 2

Answer:

$(x + iy)(5 + 3i) = 3 - 4i \\ 5x + 3xi + 5iy + 3y {i}^{2} = 3 - 4i \\ 5x - 3y + i(3x + 5y) = 3 - 4i \\ on \: comparing \\ 5x - 3y = 3......(1) \\ 3x + 5y = - 4........(2) \\ \\ 15x - 9y = 9 \\ 15x + 25y = - 20 \\ - 34y = 29 \\ = > y = - \frac{29}{34} \\ so \: 5x - 3 \times ( - \frac{29}{34} ) = 3 \\ 5x + \frac{87}{34} = 3 \\ 5x = 3 - \frac{87}{34} \\ 5x = \frac{102 - 87}{34} \\ 5x = \frac{15}{34} \\ x = \frac{3}{34}$