Re-express −18−−−−√ as a complex number with the imaginary unit i=−1−−−√ .(1 point)

1 answer

To re-express \(-\sqrt{18}\) as a complex number, we need to recognize that the square root of a negative number can be expressed using the imaginary unit \(i\), where \(i = \sqrt{-1}\).

First, we can simplify \(-\sqrt{18}\):

\[ -\sqrt{18} = -\sqrt{9 \cdot 2} = -\sqrt{9} \cdot \sqrt{2} = -3\sqrt{2} \]

Now, since \(-\sqrt{18}\) is a negative value, we can express it in terms of \(i\):

\[ -\sqrt{18} = 3\sqrt{2} \cdot (-1) = 3\sqrt{2} \cdot i^2 \]

Thus, \( -\sqrt{18} \) can be expressed as a complex number:

\[ -\sqrt{18} = 0 - 3\sqrt{2}i \]

Therefore, in the standard form of a complex number \(a + bi\), the re-expressed form of \(-\sqrt{18}\) is:

\[ 0 - 3\sqrt{2}i \]

Final answer: \[ -\sqrt{18} = 0 - 3\sqrt{2}i \]