# Math Help - Distriblutive law

1. ## Distriblutive law

I am asked to prove that addition and multiplication on C satisfy the distributive law.

I understand that I must show x(y + z) = xy + xz, but what else must I show?

2. Originally Posted by jzellt
I am asked to prove that addition and multiplication on C satisfy the distributive law.

I understand that I must show x(y + z) = xy + xz, but what else must I show?
Let $x, y, z$ all be complex numbers.

In other words, let $x = a + ib, y = c + id, z = e + ig$.

Evaluate $y + z$ then multiply the result by $x$.

Evaluate $xy + xz$.

Are these equal?

Hint: You may use the definition of multiplication of a complex number, i.e. if $z_1 = x_1 + iy_1$ and $z_2 = x_2 + iy_2$ then

$z_1z_2 = x_1x_2 - y_1y_2 + i(x_1y_2 + x_2y_1)$.