Question

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 the expression.

First, simplify \( \sqrt{-8} \):

\[
\sqrt{-8} = \sqrt{8} \cdot \sqrt{-1} = \sqrt{8}i = 2\sqrt{2}i
\]

Now substitute this back into the original expression:

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

Combine the real parts:

\[
9.2 - 3 = 6.2
\]

So the complex number simplifies to:

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

In this expression, the imaginary part is the coefficient of \(i\):

\[
\text{Imaginary part} = -2\sqrt{2}
\]

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