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Question
Find a and b if abi = 3a − b + 12i
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Solution
abi = 3a – b + 12i
0 + abi = (3a – b) + 12i
Equating real and imaginary parts, we get
3a – b = 0
∴ 3a = b ...(i)
and ab = 12
∴ b = `12/"a"` ...(ii)
Substituting b = `12/"a"` in (i), we get
3a = `12/"a"`
∴ 3a2 = 12
∴ a2 = 4
∴ a = ± 2
When a = 2, b = `12/"a" = 12/2` = 6
When a = – 2, b = `12/"a" = 12/(-2)` = – 6
∴ a = 2 and b = 6 or a = – 2 and b = – 6
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