Question

Solve the following equations for x, y ∈ R.

2x + i⁹ y(2 + i) = xi⁷ + 10i¹⁶

Answer 1

2x + i⁹y(2 + i) = xi⁷ + 10 i¹⁶

Equating real and imaginary parts, we get

2x – y = 10 ……(i)

and x + 2y = 0 ……..(ii)

Equation (i) × 2 + equation (ii) gives, we get

5x = 20

∴ x = 4

Putting x = 4 in (i), we get

2(4) – y = 10

y = 8 – 10

∴ y = -2

∴ x = 4 and y = -2