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?

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- Apr 30th 2009, 11:08 PM #1

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- Apr 30th 2009, 11:30 PM #2
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

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