To multiply the two complex numbers $(2 + 3i)$ and $(1 - 4i)$, we will use the distributive property (also known as the FOIL method).

$(2 + 3i)(1 - 4i) = 2(1) + 2(-4i) + 3i(1) + 3i(-4i)$

Now, calculate each term:

$= 2 - 8i + 3i - 12i^2$

Since $i^2 = -1$, substitute that in:

$= 2 - 8i + 3i - 12(-1)$

$= 2 - 8i + 3i + 12$

Combine like terms:

$= (2 + 12) + (-8i + 3i)$

$= 14 - 5i$

So, the product of $(2 + 3i)(1 - 4i)$ is:

$\boxed{14 - 5i}$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to further expand your understanding:

1. How do you multiply complex numbers using the FOIL method?
2. What happens when you square a complex number like $(a + bi)^2$?
3. What is the significance of $i^2 = -1$ in complex numbers?
4. How do you find the conjugate of a complex number?
5. How can you represent complex numbers on a coordinate plane?

Tip: When multiplying complex numbers, always remember that $i^2 = -1$, which turns any imaginary square into a real negative number!