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Question
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Solution
(x + 2y) + (2x − 3y)i + 4i = 5
∴ (x + 2y) + (2x − 3y)i = 5 − 4i
Equating the real and imaginary parts separately, we get,
x + 2y = 5 ....(1)
and 2x − 3y = − 4 ...(2)
Multiplying equation (1) by 2, we get,
2x + 4y = 10
Subtracting equation (2) from this equation, we get,
7y = 14
∴ y = 2
Substituting y = 2 in (1), we get,
x + 2(2) = 5
∴ x + 4 = 5
∴ x = 1
Hence, x = 1 and y = 2.
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