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Question
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
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Solution
(a + b) (2 + i) = b + 1 + (10 + 2a)i
∴ 2(a + b) + (a + b)i = (b + 1) + (10 + 2a)i
Equating real and imaginary parts, we get
2(a + b) = b + 1
∴ 2a + b = 1 ...(i)
and a + b = 10 + 2a
–a + b = 10 ...(ii)
Subtracting (i) – subtracting (ii), we get
3a = – 9
∴ a = – 3
Substituting a = – 3 in (ii), we get
– (– 3) + b = 10
∴ b = 7
a = – 3 and b = 7
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