The given expression to multiply is:

$(-9 + 4i)(-2 - 5i)$

Let's use the distributive property (also known as FOIL for binomials) to multiply the terms:

1. Multiply the real parts: $(-9)(-2) = 18$
2. Multiply the outer terms: $(-9)(-5i) = 45i$
3. Multiply the inner terms: $(4i)(-2) = -8i$
4. Multiply the imaginary parts: $(4i)(-5i) = -20i^2$

Since $i^2 = -1$, the term $-20i^2$ becomes $20$.

Now, combine all the terms:

$18 + 45i - 8i + 20 = 38 + 37i$

So, the answer in standard form is:

$38 + 37i$

Would you like further details or explanations?

Here are five related questions for further exploration:

1. What is the FOIL method and how does it work with complex numbers?
2. How do you multiply two complex numbers geometrically?
3. What is the significance of $i^2 = -1$ in complex number multiplication?
4. How can complex multiplication be visualized on the complex plane?
5. What are the properties of conjugates in complex numbers?

Tip: Always remember to simplify $i^2$ to $-1$ when multiplying imaginary parts!