Use the imaginary number 𝑖 to rewrite the expression below as a complex number. Simplify all radicals.
–
–
25

To rewrite the expression \( -\sqrt{-25} \) as a complex number, we can use the imaginary unit \( i \), where \( i = \sqrt{-1} \).

1. Start with the expression:
   \[
   -\sqrt{-25}
   \]

2. Rewrite \(\sqrt{-25}\) using the imaginary unit \(i\):
   \[
   \sqrt{-25} = \sqrt{25 \cdot (-1)} = \sqrt{25} \cdot \sqrt{-1} = 5i
   \]

3. Now, include the negative sign from the original expression:
   \[
   -\sqrt{-25} = -5i
   \]

Thus, the expression \(-\sqrt{-25}\) rewritten as a complex number is:
\[
-5i
\]

Would you like more details or have any questions about this? Here are some related questions to explore further:

1. What is the value of \( \sqrt{-9} \) in terms of \(i\)?
2. How would you express \( \sqrt{-36} \) as a complex number?
3. If \( z = 4 - 3i \), what is the magnitude of \( z \)?
4. How do you multiply two complex numbers, say \( 3 + 4i \) and \( 2 - 5i \)?
5. What is the complex conjugate of \( 7 + 2i \)?

**Tip:** Remember that \( i^2 = -1 \). This is fundamental when simplifying expressions involving imaginary numbers.

Use the imaginary number 𝑖 to rewrite the expression below as a complex number. Simplify all radicals. – – 25

Learn how to simplify the expression -√(-25) by rewriting it as a complex number using the imaginary unit i. This step-by-step solution explains key concepts related to imaginary numbers and radicals. Perfect for students in Grades 9-11.

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