Question

If z₁ = 3, z₂ = 7i, and z₃ = 5 + 4i, show that z₁(z₂ + z₃) = z₁z₂ + z₁z₃

Answer 1

z₁ = 3

z₂ = 7i

z₃ = 5 + 4i

z₂ + z₃ = – 7i + 5 + 4i

= 5 – 3i

z₁(z₂ + z₃) = 3(5 – 3i) + 15 – 9i  ........(1)

z₁z₂ = 3(– 7i)

= – 21i

z₁z₃ = 3(5 + 4i)

= 15 + 12i

z₁z₂ + z₁z₃ = – 21i + 15 + 12i

= 15 – 9i  ........(2)

∴ From 1 and 2

z₁(z₂ + z₃) = z₁z₂ + z₁z₃

Hence proved.