Find a and b if(a + ib) (1 + i) = 2 + i

1.	Find a and b if(a + ib) (1 + i) = 2 + i
Answer» (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 equations (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

Answer»

(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 equations (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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