To solve the equation \( r^2 + 100 = 0 \):

1. **Isolate \( r^2 \)** by subtracting 100 from both sides:
   \[
   r^2 = -100
   \]

2. **Take the square root** of both sides. Remember that taking the square root of a negative number introduces imaginary numbers:
   \[
   r = \pm \sqrt{-100}
   \]

3. Simplify \( \sqrt{-100} \). The square root of a negative number can be written in terms of the imaginary unit \( i \), where \( i = \sqrt{-1} \):
   \[
   \sqrt{-100} = \sqrt{100} \times \sqrt{-1} = 10i
   \]

Therefore, the solution is:
\[
r = \pm 10i
\]

This means \( r \) can be either \( 10i \) or \( -10i \).

Would you like more details, or do you have any questions?

Here are some related questions:
1. What are imaginary numbers and how are they used?
2. How do you solve quadratic equations with imaginary solutions?
3. What is the complex number plane and how does it relate to imaginary numbers?
4. How do you perform arithmetic with complex numbers?
5. What are the real-world applications of complex numbers?

**Tip:** When solving equations that involve negative square roots, always remember to express the result using imaginary numbers.

Learn how to solve the equation r^2 + 100 = 0 with detailed steps involving imaginary numbers. This problem covers quadratic equations, imaginary and complex numbers, and their applications. Suitable for students in Grades 10-12.

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