Thread: 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?

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 $\displaystyle x, y, z$ all be complex numbers.

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

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

Evaluate $\displaystyle xy + xz$.

Are these equal?


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

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