Question

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

9.2
9.2

6i2–√
6 i square root of 2

−6i2–√
negative 6 i square root of 2

−3i8–√

Answer 1

To simplify the complex number \( 9.2 - 3 - 8^{-\frac{1}{2}} \):

First, we find \( 8^{-\frac{1}{2}} \), which is the same as \( \frac{1}{\sqrt{8}} \). We can simplify \( \sqrt{8} \) as follows:

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

So:

\[
8^{-\frac{1}{2}} = \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}} = \frac{\sqrt{2}}{4}
\]

Now, substituting this back into the original expression:

\[
9.2 - 3 - \frac{\sqrt{2}}{4}
\]

First, calculate \( 9.2 - 3 \):

\[
9.2 - 3 = 6.2
\]

So we have:

\[
6.2 - \frac{\sqrt{2}}{4}
\]

This is still a real number, as all terms are real numbers. Hence, there is no imaginary component in this expression.

From the provided responses, it seems we are supposed to represent our answers in a particular way. However, since we simplified the expression and found that it does not contain any \( i \) (the imaginary unit), we can conclude that the imaginary part is \( 0 \).

Thus, the correct answer choice does not seem to correspond with any of the options listed, as all the given options include imaginary terms.

So the imaginary part is:

\[
0
\]