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Question
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
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Solution
(4 − 5i)x + (2 + 3i)y = 10 − 7i
∴ (4x + 2y) + (3y − 5x) i = 10 − 7i
Equating real and imaginary parts, we get
4x + 2y = 10
i.e., 2x + y = 5 ...(i)
and 3y − 5x = −7 ...(ii)
Multiply equation (i) by 3:
6x + 3y = 15 ...(iii)
Subtract equation (ii) from equation (iii):
(6x + 3y) − (3y − 5x) = 15 − (−7)
11x = 22
∴ x = 2
Substitute x = 2 in equation (i):
2(2) + y = 5
∴ y = 1
∴ x = 2 and y = 1
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