Question

Which of the following re-expresses the negative square root −5−20−−−−√%0D%0A−%0D%0A5%0D%0A−%0D%0A20%0D%0A as a complex number in the standard form a+bi?(1 point)%0D%0AResponses%0D%0A%0D%0A−5i5–√%0D%0A−%0D%0A5%0D%0A𝑖%0D%0A5%0D%0Anegative 5 i square root of 5%0D%0A%0D%0A−10i5–√%0D%0A−%0D%0A10%0D%0A𝑖%0D%0A5%0D%0Anegative 10 i square root of 5%0D%0A%0D%0A5i10−−√%0D%0A5%0D%0A𝑖%0D%0A10%0D%0A5 i square root of 10%0D%0A%0D%0A−20i5–√

Answer 1

To re-express the expression \(-\sqrt{-5 - 20}\) as a complex number in the standard form \(a + bi\), we start by simplifying the square root.

First, calculate the expression under the square root:

\[
-5 - 20 = -25
\]

Now we have:

\[
-\sqrt{-25}
\]

The square root of a negative number can be expressed using the imaginary unit \(i\), where \(i = \sqrt{-1}\). Thus, we can rewrite the square root:

\[
\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i
\]

So we have:

\[
-\sqrt{-25} = -5i
\]

Thus, the expression \(-\sqrt{-5 - 20}\) simplifies to:

\[
-5i
\]

This can be expressed in standard form \(a + bi\) as:

\[
0 - 5i
\]

Therefore, the answer is:

\(-5i\)