Find a and b ifabi = 3a – b + 12i

1.	Find a and b ifabi = 3a – b + 12i
Answer» abi = 3a – b + 12i ∴ 0 + abi = (3a – b) + 12i Equating real and imaginary parts, we get 3a – b = 0 ∴ 3a = b …..(i) and ab = 12 ∴ b = 12/a……..(ii) Substituting b = 12/a in (i), we get 3a = 12/a 3a²= 12 a² = 4 a = ±2 When a = 2, b = 12/a = 12/2 = 6 When a = -2, b = 12/a = 12/-2 = -6 ∴ a = 2 and b = 6 or a = -2 and b = -6

Answer»

abi = 3a – b + 12i

∴ 0 + abi = (3a – b) + 12i

Equating real and imaginary parts, we get

3a – b = 0

∴ 3a = b …..(i)

and ab = 12

∴ b = 12/a……..(ii)

Substituting b = 12/a in (i), we get

3a = 12/a

3a²= 12

a² = 4

a = ±2

When a = 2, b = 12/a = 12/2 = 6

When a = -2, b = 12/a = 12/-2 = -6

∴ a = 2 and b = 6 or a = -2 and b = -6

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