This problem involves multiplying two complex numbers. Let’s calculate:

We are given $(6 + 2i)(-7 - 5i)$.

Step 1: Use the distributive property (FOIL method):

$(6 + 2i)(-7 - 5i) = (6)(-7) + (6)(-5i) + (2i)(-7) + (2i)(-5i)$

Step 2: Multiply each term:

1. $6 \times -7 = -42$
2. $6 \times -5i = -30i$
3. $2i \times -7 = -14i$
4. $2i \times -5i = -10i^2$

Step 3: Combine the terms:

$-42 - 30i - 14i - 10i^2$

Step 4: Simplify $i^2 = -1$:

$-10i^2 = -10(-1) = 10$

So the expression becomes: $-42 - 30i - 14i + 10$

Step 5: Combine like terms:

1. Real part: $-42 + 10 = -32$
2. Imaginary part: $-30i - 14i = -44i$

Final Answer:

$(6 + 2i)(-7 - 5i) = -32 - 44i$

Would you like further clarification or additional examples?

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Here are five related questions for practice:

1. How do you multiply $(3 + 4i)(1 - 2i)$?
2. What happens when you square a complex number like $(1 + i)^2$?
3. How can you find the magnitude of a complex number $-32 - 44i$?
4. What is the geometric interpretation of multiplying complex numbers?
5. How would you divide $(6 + 2i)$ by $(-7 - 5i)$?

Tip: Always simplify $i^2$ as $-1$ when multiplying or squaring complex numbers to avoid errors!