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To solve the equation \( x^2 + 9 = 0 \), let's go through the steps:

1. **Rewrite the equation:** 
   \[
   x^2 + 9 = 0
   \]
   Subtract 9 from both sides to isolate \( x^2 \):
   \[
   x^2 = -9
   \]

2. **Solve for \( x \) by taking the square root of both sides:**
   \[
   x = \pm \sqrt{-9}
   \]
   Since \(-9\) is negative, the square root involves imaginary numbers. Recall that \( \sqrt{-1} = i \), where \( i \) is the imaginary unit.

3. **Simplify the square root of \(-9\):**
   \[
   x = \pm 3i
   \]

Thus, the solution set for the equation is \( \{3i, -3i\} \).

### Answer
The correct option is:
**B. \( \{3i, -3i\} \)**

Would you like more details on imaginary numbers or have any questions?

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Here are some related questions for further understanding:

1. What are imaginary numbers, and how do they differ from real numbers?
2. How do you solve equations with negative square roots?
3. What does the symbol \( i \) represent, and why is it important in complex numbers?
4. How can you determine if an equation has complex solutions?
5. Why does squaring a number result in a positive value for real numbers but not for complex numbers?

**Tip:** When taking the square root of a negative number, remember to include the imaginary unit \( i \) in your solution.

What is the solution set of the equation x^2 + 9 = 0?

Understand how to find the solution set for x^2 + 9 = 0, involving complex numbers. This problem highlights key algebraic concepts and introduces imaginary numbers, suitable for students in Grades 9-10.

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