Express  
√
−
5
   as a complex number, in terms of i: 5

√
−
5
   = 

To express \( \sqrt{-5} \) as a complex number, we can rewrite it in terms of \( i \), the imaginary unit, where \( i = \sqrt{-1} \).

1. Start with the expression:  
   \[
   \sqrt{-5}
   \]

2. Rewrite \( -5 \) as \( -1 \cdot 5 \):
   \[
   \sqrt{-5} = \sqrt{-1 \cdot 5}
   \]

3. Use the property \( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \):
   \[
   \sqrt{-5} = \sqrt{-1} \cdot \sqrt{5}
   \]

4. Substitute \( \sqrt{-1} = i \):
   \[
   \sqrt{-5} = i \cdot \sqrt{5}
   \]

So, the answer is:
\[
\sqrt{-5} = i \sqrt{5}
\]

Would you like a more detailed explanation, or do you have any questions?

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Here are five related questions to deepen understanding:

1. How would you express \( \sqrt{-10} \) as a complex number?
2. What is the general form for the square root of any negative number in terms of \( i \)?
3. Can you simplify expressions involving higher powers of \( i \)?
4. What are some practical applications of imaginary numbers in physics or engineering?
5. How do complex numbers help in solving quadratic equations with no real solutions?

**Tip:** When simplifying square roots of negative numbers, remember that \( i \) allows you to express any negative square root in terms of positive values.

Express √−5 as a complex number, in terms of i.

Learn how to express the square root of −5 as a complex number in terms of i. This solution covers key concepts in complex numbers, including the imaginary unit and properties of square roots. Perfect for high school students in Grades 10-12.

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√ − 5

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