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The problem is asking you to multiply two complex numbers, \( (10 - 3i)(5 + 2i) \).

### Step-by-Step Solution:

1. **Use the distributive property (FOIL method)** to multiply:
   \[
   (10 - 3i)(5 + 2i) = 10(5) + 10(2i) - 3i(5) - 3i(2i)
   \]

2. **Simplify each term:**
   \[
   = 50 + 20i - 15i - 6i^2
   \]

3. **Combine like terms:**
   \[
   = 50 + (20i - 15i) - 6i^2
   = 50 + 5i - 6i^2
   \]

4. **Recall that \( i^2 = -1 \):**
   \[
   -6i^2 = -6(-1) = 6
   \]

5. **Simplify the expression further:**
   \[
   50 + 5i + 6 = 56 + 5i
   \]

### Final Answer:
The product is \( 56 + 5i \), so the correct option is the first one: **\( 56 + 5i \)**.

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Do you need further details on any of the steps? Here are some related questions:

1. How do you multiply two complex numbers in general?
2. What is the significance of \( i^2 = -1 \) in complex number multiplication?
3. Can you explain the FOIL method in more detail?
4. What happens when you multiply complex conjugates?
5. How would you add or subtract complex numbers?

**Tip:** Always remember that \( i^2 = -1 \) when dealing with imaginary numbers.

Learn how to multiply the complex numbers (10 - 3i) and (5 + 2i) using the FOIL method. This step-by-step guide covers key concepts in complex numbers, including how to combine real and imaginary terms. Suitable for students in Grades 9-11.

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