Distriblutive law

**jzellt** · Apr 30th 2009, 11:08 PM

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?

**Prove It** · Apr 30th 2009, 11:30 PM

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

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

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