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

Answer 1

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

1. Recognize that \( \sqrt{-8} \) can be rewritten using imaginary numbers: \[ \sqrt{-8} = \sqrt{8} \cdot \sqrt{-1} = \sqrt{8} i = 2\sqrt{2} i. \]

2. Substitute this into the expression: \[ 9.2 - 3 - \sqrt{-8} = 9.2 - 3 - 2\sqrt{2} i. \]

3. Simplify the real part: \[ 9.2 - 3 = 6.2. \]

So now we have: \[ 6.2 - 2\sqrt{2} i. \]

4. The final form of the complex number is \( 6.2 - 2\sqrt{2} i \).

The imaginary part of this complex number is: \[ -2\sqrt{2}. \]

Thus, the answer is: \[ \boxed{-2\sqrt{2}}. \]