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Question
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
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Solution
`(x + "i"y)/(2 + 3"i")` = 7 – i
∴ x + iy = (7 – i)(2 + 3i)
∴ x + iy = 14 + 21i – 2i – 3i2
∴ x + iy = 14 + 19i + 3 ...[∵ i2 = – 1]
∴ x + iy = 17 + 19i
Equating the real and imaginary parts separately, we get,
x = 17, y = 19
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