What is the imaginary part of the simplest form of the complex number 9.2−3−8−−−√ ?(1 point)

1 answer

To find the imaginary part of the complex number \( 9.2 - 3 - \sqrt{-8} \), we first need to simplify \( \sqrt{-8} \).

Recall that \( \sqrt{-8} \) can be expressed as:

\[ \sqrt{-8} = \sqrt{8} \times \sqrt{-1} = \sqrt{8} i \]

Since \( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \), we have:

\[ \sqrt{-8} = 2\sqrt{2} i \]

Now, substitute this back into the expression:

\[ 9.2 - 3 - \sqrt{-8} = 9.2 - 3 - 2\sqrt{2} i \]

Now simplify the real part:

\[ 9.2 - 3 = 6.2 \]

Thus, we can rewrite the complex number as:

\[ 6.2 - 2\sqrt{2} i \]

Here, the imaginary part is:

\[ -2\sqrt{2} \]

Therefore, the imaginary part of the complex number \( 9.2 - 3 - \sqrt{-8} \) is \(-2\sqrt{2}\).