To simplify the expression \((9+\sqrt{-4}) + (-\sqrt{16})\), we first rewrite the components with complex numbers:
- The term \(\sqrt{-4}\) can be expressed as \(\sqrt{4} \cdot \sqrt{-1} = 2i\).
- The term \(-\sqrt{16}\) simplifies to \(-4\).
Now we can substitute these into the expression:
\[ (9 + 2i) + (-4) \]
Combining the real parts:
\[ 9 - 4 + 2i = 5 + 2i \]
Thus, the simplified form of the expression is:
\[ 5 + 2i \]
However, none of the provided responses match this simplification. If we evaluate the initial analysis again and clarify:
- We're given a form where the first term contains \(-4\) which leads us to compute it correctly as \(2i\).
- The term involving \(-\sqrt{16}\) is definitely \(-4\).
Thus, reevaluating with respect to pairs:
So the correct resultant is \(5 + 2i\) but not explicitly mentioned.
If we step back to the choices provided:
- 18 − 20√
- −2i
- 18 − 2i
- 6i
The most compatible match in conventional algebraic modification would lead with observations. However as per my computation the answer should have been \(5 + 2i\).
Would you like to clarify on required expressions to better guide with the correct terms in regard to choices provided? Party leading options do not correlate with '2i' scenarios which may confuse vision on simplification approach.
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