To perform the operation $(8 - 12i)(-5 - 7i)$ and express the answer as a complex number, we'll use the distributive property (FOIL method):

$(8 - 12i)(-5 - 7i) = 8(-5) + 8(-7i) - 12i(-5) - 12i(-7i)$

Now, let's calculate each term:

1. $8(-5) = -40$
2. $8(-7i) = -56i$
3. $-12i(-5) = 60i$
4. $-12i(-7i)$

The term $-12i(-7i)$ simplifies as follows:

$-12i(-7i) = 84i^2$

Since $i^2 = -1$, this becomes:

$84i^2 = 84(-1) = -84$

Now, combine all the terms:

$-40 - 56i + 60i - 84$

Combine the real and imaginary parts:

• Real part: $-40 - 84 = -124$
• Imaginary part: $-56i + 60i = 4i$

So, the simplified form of the expression is:

$\boxed{-124 + 4i}$

Would you like more details or have any questions about the process? Here are some related questions for further practice:

1. Simplify $(3 + 2i)(4 - 5i)$.
2. Find the product of $(7 - i)(3 + 4i)$.
3. Simplify $(2 - 3i)^2$.
4. Perform the operation and simplify $(5 + 6i)(-2 + 9i)$.
5. Multiply $(1 - 2i)(-3 + 7i)$ and simplify.

Tip: When multiplying complex numbers, always remember to apply the distributive property and simplify using $i^2 = -1$.