Question

Find a and b if

(a + ib) (1 + i) = 2 + i

Answer 1

(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