Find a and b if (a + b) (2 + i) = b + 1 + (10 + 2a)i

1.	Find a and b if (a + b) (2 + i) = b + 1 + (10 + 2a)i
Answer» (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 equation (ii) from (i), we get 3a = -9 ∴ a = -3 Substituting a = – 3 in (ii), we get -(-3) + b = 10 ∴ b = 7 ∴ a = -3 and b = 7

Answer»

(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 equation (ii) from (i), 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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