要计算复数 $z_1 = 4 + 2i$ 和 $z_2 = 1 - 3i$ 的乘积 $z_1 \cdot z_2$，我们使用复数乘法规则：

$z_1 \cdot z_2 = (4 + 2i)(1 - 3i)$

我们用分配律展开这个表达式：

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

这将得到：

$= 4 - 12i + 2i - 6i^2$

由于 $i^2 = -1$，我们可以进一步简化：

$= 4 - 12i + 2i - 6(-1)$

$= 4 - 12i + 2i + 6$

$= 10 - 10i$

因此，复数的乘积是：

$z_1 \cdot z_2 = 10 - 10i$

Would you like more details or have any questions about this solution? Here are five more questions you might be interested in:

1. How do you divide complex numbers?
2. What is the geometric interpretation of complex number multiplication?
3. How do you find the magnitude of a complex number?
4. How do you add and subtract complex numbers?
5. How do you convert complex numbers between rectangular and polar form?

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