Question

Find a and b if

abi = 3a – b + 12i

Answer 1

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