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Question
Find the value of x and y which satisfy the following equation (x, y∈R).
If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y
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Solution
x + 2i + 15i6y = 7x + i3 (y + 4)
∴ x + 2i – 15y = 7x – i(y + 4) ...[∵ i6 = (i2)3 = – 1, i3 = – i]
∴ x + 2i – 15y – 7x + i(y + 4) = 0
∴ (– 6x – 15y) + (2 + y + 4)i = 0 + 0.i
Equating the real and imaginary parts, we get,
∴ – 6x – 15y = 0 ...(1)
and y + 6 = 0 ...(2)
From (2), y = – 6
Substituting y = – 6 in (1), we get,
– 6x + 90 = 0
∴ x = 15
∴ x + y = 15 – 6 = 9
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