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Question
Find a and b if (a + ib) (1 + i) = 2 + i
Solution
(a + ib) (1 + i) = 2 + i
∴ a + ai + bi + bi2 = 2 + i
∴ a + (a + b)i + b(–1) = 2 + i …[∵ i2 = – 1]
∴ (a – b) + (a + b)i = 2 + i
Equating real and imaginary parts, we get
a – b = 2 ...(i)
a + b = 1 ...(ii)
Adding equation (i) and (ii), we get
2a = 3
∴ a = `3/2`
Substituting a = `3/2` in (ii),we get
`3/2 +"b"` = 1
∴ b = `1 - 3/2 = -1/2`
a = `3/2`and b = `-1/2`.
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