\( (-3+\sqrt{-16})^{2} \) \( \begin{array}{l}(-3+\sqrt{-16})^{2}=\square \\ \text { (Simplify your answer. Type your answer in the form a indicated operations. } \\ \end{array} \)

To simplify \( (-3+\sqrt{-16})^{2} \), we first recognize that \( \sqrt{-16} \) can be rewritten using imaginary numbers. Recall that \( \sqrt{-16} = \sqrt{16} i = 4i \). Now, substituting back into the expression, we have: \[ (-3 + 4i)^{2} \] Next, we apply the expansion formula \( (a+b)^2 = a^2 + 2ab + b^2 \): \[ = (-3)^2 + 2(-3)(4i) + (4i)^2 \] Calculating each term: \[ (-3)^2 = 9, \] \[ 2(-3)(4i) = -24i, \] \[ (4i)^2 = 16i^2 = 16(-1) = -16. \] Now, combine all the terms: \[ 9 - 24i - 16 = -7 - 24i. \] Thus, the simplified answer is: \[ (-3+\sqrt{-16})^{2} = -7 - 24i. \]