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To solve the problem \(9i(5 - 8i)\), we need to use the distributive property and simplify the result. Let's work through it step-by-step.

1. **Apply the Distributive Property**:
   \[
   9i(5 - 8i) = 9i \cdot 5 - 9i \cdot 8i
   \]

2. **Multiply Each Term**:
   - For the first term: \(9i \cdot 5 = 45i\)
   - For the second term: \(9i \cdot -8i = -72i^2\)

3. **Simplify Using \(i^2 = -1\)**:
   Since \(i^2 = -1\), we can replace \(i^2\) with \(-1\) in the expression:
   \[
   -72i^2 = -72(-1) = 72
   \]

4. **Combine Terms**:
   Now we have:
   \[
   45i + 72
   \]

5. **Write in Standard Form \(a + bi\)**:
   The answer is:
   \[
   72 + 45i
   \]

So, the simplified answer in the form \(a + bi\) is:

\[
\boxed{72 + 45i}
\]

Would you like a detailed explanation of any specific part of this solution?

Here are some additional questions related to this problem:
1. What is the significance of \(i^2 = -1\) in complex number calculations?
2. How do you multiply two complex numbers in general?
3. What are the real and imaginary components of \(72 + 45i\)?
4. How would you represent the complex number \(72 + 45i\) on the complex plane?
5. What happens when you multiply a complex number by a purely imaginary number?

**Tip:** When working with complex numbers, always remember that \(i^2 = -1\); this identity is key to simplifying terms involving \(i\).

Multiply 9i(5 - 8i) and simplify your answer in the form a + bi.

Learn how to multiply complex numbers with a detailed solution to 9i(5 - 8i). This problem covers concepts in complex number multiplication and the imaginary unit i properties. Suitable for high school students in Grades 10-12.

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