Use the imaginary number $$ i $$ to rewrite the expression below as a complex number. Sir all radicals. $$ -1-\sqrt{-5} $$

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UpStudy AI · Accepted Answer

To express the given expression $$ -1 - \sqrt{-5} $$ as a complex number using the imaginary unit $$ i $$, follow these steps:

1. **Express the Square Root of a Negative Number:**
   
   The square root of a negative number can be written in terms of $$ i $$, where $$ i = \sqrt{-1} $$. Specifically:
   $$
   \sqrt{-5} = \sqrt{5} \cdot \sqrt{-1} = \sqrt{5} \cdot i = i\sqrt{5}
   $$

2. **Substitute Back into the Original Expression:**
   
   Replace $$ \sqrt{-5} $$ with $$ i\sqrt{5} $$ in the original expression:
   $$
   -1 - \sqrt{-5} = -1 - i\sqrt{5}
   $$

3. **Write in Standard Complex Form:**
   
   The standard form of a complex number is $$ a + bi $$, where $$ a $$ is the real part and $$ b $$ is the imaginary part. Thus:
   $$
   -1 - i\sqrt{5}
   $$

So, the expression $$ -1 - \sqrt{-5} $$ written as a complex number is:

$$
-1 - i\sqrt{5}
$$

**Final Answer:**
$$
-1 - i\,\sqrt{5}
$$
$$ -1 - i\sqrt{5} $$

Use the imaginary number to rewrite the expression below as a complex number. Sir
all radicals.

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Use the imaginary number to rewrite the expression below as a complex number. Sir all radicals.