To solve $(4 - 2i)(8 + 7i)$, we will expand and simplify using the distributive property and the fact that $i^2 = -1$.

Step 1: Expand the expression

$(4 - 2i)(8 + 7i) = 4(8) + 4(7i) - 2i(8) - 2i(7i)$

Simplify each term: $= 32 + 28i - 16i - 14i^2$

Step 2: Simplify further

Combine the real and imaginary parts: $32 + (28i - 16i) - 14i^2 = 32 + 12i - 14i^2$

Since $i^2 = -1$, substitute $-1$ for $i^2$: $= 32 + 12i - 14(-1)$

$= 32 + 12i + 14$

Step 3: Final result

Combine the real parts: $= 46 + 12i$

Thus, the simplified result is: $\boxed{46 + 12i}$

Let me know if you want further clarifications! Here are some related questions:

1. How do you multiply two complex numbers geometrically?
2. What are the rules for simplifying complex numbers involving $i^2$?
3. Can this be represented in polar form? How would you do it?
4. How does the distributive property apply to complex numbers?
5. What are some practical applications of multiplying complex numbers?

Tip: Always check for $i^2 = -1$ during simplifications to avoid errors in handling imaginary components!