To multiply and simplify the given complex numbers $(1 - 5i) \cdot (3 - 2i)$, we will use the distributive property, often referred to as the FOIL (First, Outer, Inner, Last) method when dealing with binomials.

Let's proceed step-by-step:

1. First: Multiply the first terms from each binomial: $1 \cdot 3 = 3$

2. Outer: Multiply the outer terms: $1 \cdot (-2i) = -2i$

3. Inner: Multiply the inner terms: $-5i \cdot 3 = -15i$

4. Last: Multiply the last terms: $-5i \cdot (-2i) = 10i^2$

Next, we simplify by combining like terms. But first, recall that $i^2 = -1$, so: $10i^2 = 10(-1) = -10$

Now, let's add up all the terms: $3 - 2i - 15i - 10$

Combine the real and imaginary parts: $(3 - 10) + (-2i - 15i) = -7 - 17i$

Thus, the simplified result of multiplying $(1 - 5i) \cdot (3 - 2i)$ is: $\boxed{-7 - 17i}$

Would you like to see further details or have any questions?

Here are 5 related questions:

1. How do you add and subtract complex numbers?
2. What is the conjugate of a complex number, and how is it used in division?
3. How do you find the modulus of a complex number?
4. What is the polar form of a complex number?
5. How do you multiply complex numbers in polar form?

Tip: Always remember that $i^2 = -1$. This is crucial for simplifying expressions involving complex numbers.