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

Question

.(1 point)
Responses

6i
6 i

−2i
negative 2 i

18−−20−−−−√
18 minus Start Root negative 20 End Root

18−2i
18 minus 2 i

Answer 1

To simplify the expression \( (9 + \sqrt{-4}) + \left(-9 + \sqrt{-16}\right) \), we can first rewrite the square roots of the negative numbers in terms of \( i \).

Recall that:

• \(\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i\)
• \(\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i\)

Now, substituting these values into the expression:

\[ (9 + 2i) + (-9 + 4i) \]

Now we can simplify this expression:

\[ 9 - 9 + 2i + 4i = 0 + 6i = 6i \]

So the simplified result is:

\[ \boxed{6i} \]