Solve the following equations for x, y ∈ R. \(\frac{x+iy}{2+3i}=7-i

1.	Solve the following equations for x, y ∈ R. \(\frac{x+iy}{2+3i}=7-i\)(x + iy)/(2 + 3i) = 7 - i
Answer» \(\frac{x+iy}{2+3i}=7-i\) x + iy = (7 – i)(2 + 3i) x + iy = 14 + 21i – 2i – 3i² x + iy = 14 + 19i – 3(-1) x + iy = 17 + 19i Equating real and imaginary parts, we get ∴ x = 17 and y = 19

Solve the following equations for x, y ∈ R. \(\frac{x+iy}{2+3i}=7-i\)(x + iy)/(2 + 3i) = 7 - i

Answer»

\(\frac{x+iy}{2+3i}=7-i\)

x + iy = (7 – i)(2 + 3i)

x + iy = 14 + 21i – 2i – 3i²

x + iy = 14 + 19i – 3(-1)

x + iy = 17 + 19i

Equating real and imaginary parts, we get

∴ x = 17 and y = 19