Look for perfect cubes within each term. This will allow us to factor out of the radical.

Simplify.

We can use Heron's formula to find the area of the triangle. We can let a = 6, b = 10, and c = 12.

In order to find s, we need to find one half of the perimeter. The perimeter is the sum of the lengths of the sides of the triangle.

Perimeter = a + b + c = 6 + 10 + 12 = 28

In order to find s, we must multiply the perimeter by one-half, which would give us (1/2)(28), or 14.

Now that we have a, b, c, and s, we can calculate the area using Heron's formula.

If you don't already have the pattern memorized, use FOIL. It's best to write out the parentheses twice (as below) to avoid mistakes:

This gives us roots of

The product of with each of these gives us:

The sum of these 4 is:

What we notice is that each of the roots has a negative. It thus makes sense that they will all cancel out. Rather than going through all the multiplication, we can instead look at the very beginning setup, which we can simplify using the distributive property:

Distribute (3 + 4i)(4 - 3i)

3(4) + 3(-3i) + 4i(4) + 4i(-3i)

12 - 9i + 16i -12i2

12 + 7i - 12(-1)

12 + 7i + 12

24 + 7i

Rewrite in their imaginary terms.

This gives us roots of

The product of with each of these gives us:

The sum of these 4 is:

What we notice is that each of the roots has a negative. It thus makes sense that they will all cancel out. Rather than going through all the multiplication, we can instead look at the very beginning setup, which we can simplify using the distributive property:

, so

, so

, and

Rationalize the denominator by multiplying both numerator and denominator by the complex conjugate of the latter, which is :

Use FOIL:

Combine like terms:

But since , we know

Apply the Power of a Product Rule:

,

and

,

so, substituting and evaluating: