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Solve the following equations for x, y ∈ R.

2x + i9 y(2 + i) = xi7 + 10i16

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Best answer

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

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