Let's multiply the two complex numbers $(-3 + 2i)(-4 + 4i)$ step by step.

Step 1: Expand the product using distributive property

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

Step 2: Compute individual terms

• $(-3)(-4) = 12$
• $(-3)(4i) = -12i$
• $(2i)(-4) = -8i$
• $(2i)(4i) = 8i^2$

Step 3: Use $i^2 = -1$

$8i^2 = 8(-1) = -8$

Step 4: Combine real and imaginary parts

Now, group the real and imaginary terms: $12 - 8 + (-12i - 8i)$ $(12 - 8) + (-12i - 8i) = 4 - 20i$

Final Answer

The product of $(-3 + 2i)(-4 + 4i)$ is: $4 - 20i$

Thus, the answer in standard form is: $4 - 20i$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you add two complex numbers?
2. What is the geometric meaning of multiplying complex numbers?
3. What happens when you multiply a complex number by its conjugate?
4. How do you convert a complex number from rectangular to polar form?
5. What are the rules for dividing two complex numbers?

Tip: When multiplying complex numbers, always remember to simplify $i^2$ to $-1$.