Question

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

Answer 1

To find the simplest form of the complex number \( 9.2 - \sqrt{-8} \), we first need to simplify the square root of the negative number.

The square root of \(-8\) can be expressed as follows:

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

Now, simplify \( \sqrt{8} \):

\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

Thus, we have:

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

Now, replacing \(\sqrt{-8}\) in the original expression \( 9.2 - \sqrt{-8} \):

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

From this expression, we can identify the real and imaginary parts. The real part is \( 9.2 \) and the imaginary part is \( -2\sqrt{2} \).

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

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