Question

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

18−2i
18 minus 2 i

−2i
negative 2 i

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

6i

Answer 1

To simplify the expression \((9 + \sqrt{-4}) + (-\sqrt{16})\), we first rewrite it in terms of complex numbers.

1. **Identify the square roots**:
- \(\sqrt{-4} = 2i\) (since \(\sqrt{-1} = i\) and \(\sqrt{4} = 2\))
- \(-\sqrt{16} = -4\) (since \(\sqrt{16} = 4\))

2. **Substituting the square roots back into the expression**:
- \((9 + \sqrt{-4}) + (-\sqrt{16}) = (9 + 2i) - 4\)

3. **Combine like terms**:
- \(9 - 4 + 2i = 5 + 2i\)

Based on the options provided, none of them directly match \(5 + 2i\). However, if the expression you meant to simplify was different or if there may have been a mistake in the original problem, feel free to clarify!

If we look for the correct simplification from the original expression given (\((9 - \sqrt{-4}) + (-\sqrt{16})\)), I will carry on.

- In case this is the true intended equation, we should substitute \((9 - 2i) - 4 = 5 - 2i\).

However, if we consider the response format you provided, it seems \(18 - 2i\) might not represent the correct simplification as described.

Please review and ensure that all steps align, or provide further context needed for your query!