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The question in the image asks you to evaluate the expression:

\[
(8 - 3i) \times (-2 - 3i)
\]

and write the result in the form \(a + bi\), where \(a\) and \(b\) are real numbers, and \(i\) is the imaginary unit.

### Step-by-Step Solution:

1. **Use the distributive property (FOIL method):**
   Multiply each term in the first complex number by each term in the second complex number:

\[
(8 - 3i) \times (-2 - 3i) = 8 \times (-2) + 8 \times (-3i) + (-3i) \times (-2) + (-3i) \times (-3i)
\]

2. **Calculate each multiplication:**
   - \(8 \times (-2) = -16\)
   - \(8 \times (-3i) = -24i\)
   - \((-3i) \times (-2) = 6i\)
   - \((-3i) \times (-3i) = 9i^2\) (Note: \(i^2 = -1\))

   Therefore:
   \[
   (8 - 3i) \times (-2 - 3i) = -16 - 24i + 6i + 9i^2
   \]

3. **Simplify the expression:**
   - Combine like terms: \(-24i + 6i = -18i\)
   - Replace \(i^2\) with \(-1\): \(9i^2 = 9 \times (-1) = -9\)

   Now, the expression becomes:
   \[
   -16 - 18i - 9
   \]

4. **Final simplification:**
   \[
   (-16 - 9) - 18i = -25 - 18i
   \]

Thus, the result is:

\[
-25 - 18i
\]

Would you like further clarification or details on this? Here are some related questions you might find useful:

1. How do you multiply two complex numbers in general?
2. What is the significance of the imaginary unit \(i\) and why does \(i^2 = -1\)?
3. How do you convert a complex number to polar form?
4. How can we represent complex numbers graphically?
5. What are the real and imaginary parts of a complex number?

**Tip:** When multiplying complex numbers, always remember that \(i^2 = -1\), which helps simplify the result!

Evaluate the expression (8 - 3i)(-2 - 3i) and write the result in the form a + bi.

Learn how to multiply two complex numbers using the distributive property (FOIL method). This step-by-step guide explains how to simplify the expression (8 - 3i)(-2 - 3i) and write the result in the form a + bi. Suitable for high school students learning about complex numbers and algebra.

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