Question

Express $9.2 - 3 √(-8)$ as a complex number in the form of $a + bi$. What is the imaginary term?
\square

Answer 1

To express the expression \( 9.2 - 3 \sqrt{-8} \) as a complex number in the form of \( a + bi \), we first need to simplify the term \( \sqrt{-8} \).

Recall that:

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

Next, we calculate \( \sqrt{8} \):

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

Thus, we can write:

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

Now we substitute this back into our original expression:

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

Calculating the multiplication:

\[
-3(2 \sqrt{2} i) = -6 \sqrt{2} i
\]

Putting it all together gives us:

\[
9.2 - 6 \sqrt{2} i
\]

This can be expressed in the standard form of a complex number \( a + bi \):

\[
9.2 + (-6 \sqrt{2}) i
\]

From this, we identify the real part \( a = 9.2 \) and the imaginary part \( b = -6 \sqrt{2} \).

Therefore, the imaginary term of the complex number is:

\[
\boxed{-6 \sqrt{2}}
\]