e the imaginary number i to rewrite the expression below as a complex number. Simp radicals. $$ -\sqrt{-66} $$

Question

UpStudy AI · Accepted Answer

To express the expression $$-\sqrt{-66}$$ as a complex number using the imaginary unit $$i$$ (where $$i = \sqrt{-1}$$), follow these steps:

1. **Understand the Imaginary Unit ($$i$$):**
   
   The imaginary unit $$i$$ is defined as:
   $$
   i = \sqrt{-1}
   $$
   This allows us to handle square roots of negative numbers by expressing them in terms of $$i$$.

2. **Rewrite $$-\sqrt{-66}$$ Using $$i$$:**

Start with the original expression:
   $$
   -\sqrt{-66}
   $$
   
   Break down the square root of the negative number:
   $$
   \sqrt{-66} = \sqrt{66 \times (-1)} = \sqrt{66} \times \sqrt{-1}
   $$
   
   Substitute $$\sqrt{-1}$$ with $$i$$:
   $$
   \sqrt{-66} = \sqrt{66} \times i = i\sqrt{66}
   $$
   
   Now, include the negative sign from the original expression:
   $$
   -\sqrt{-66} = -i\sqrt{66}
   $$
   
3. **Final Complex Number:**

The expression $$-\sqrt{-66}$$ expressed as a complex number is:
   $$
   -i\sqrt{66}
   $$
   
   This is in the standard form $$a + bi$$, where $$a = 0$$ and $$b = -\sqrt{66}$$.

4. **Summary:**

$$
   -\sqrt{-66} = -i\sqrt{66}
   $$
   
   This represents the original expression as a complex number with an imaginary component.
$$-\sqrt{-66}$$ can be written as $$-i\sqrt{66}$$.

e the imaginary number i to rewrite the expression below as a complex number. Simp radicals. \( -\sqrt{-66} \)

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions