Question

Use the properties of complex numbers to simplify (9+−4−−−√)+(−9−−16−−−−√)
(
9
+
−
4
)
+
(
−
9
−
−
16
)
.(1 point)
Responses

−2i
−
2
𝑖
negative 2 i

6i
6
𝑖
6 i

18−−20−−−−√
18
−
−
20
18 minus square root of negative 20

18−2i

Answer 1

To simplify the expression \((9 + \sqrt{-4}) + (-9 - \sqrt{-16})\), we need to express the square roots of the negative numbers in terms of complex numbers.

First, we can express \(\sqrt{-4}\) and \(\sqrt{-16}\) as follows:

\[
\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i
\]

\[
\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i
\]

Now we can substitute these values into the original expression:

\[
(9 + \sqrt{-4}) + (-9 - \sqrt{-16}) = (9 + 2i) + (-9 - 4i)
\]

Next, we can combine the real and imaginary parts:

For the real part:
\[
9 - 9 = 0
\]

For the imaginary part:
\[
2i - 4i = -2i
\]

Putting it all together, we have:

\[
0 - 2i = -2i
\]

So, the simplified expression is:

\(-2i\)