Perform the indicated operations and express the result as a simplified complex number. \[ 2 \sqrt{-75}+8 \sqrt{25} \] \( \square \)

To simplify the expression \( 2 \sqrt{-75} + 8 \sqrt{25} \), we start by breaking down each term. First, for \( \sqrt{-75} \): \[ \sqrt{-75} = \sqrt{75} \cdot \sqrt{-1} = \sqrt{75}i = \sqrt{25 \cdot 3}i = 5\sqrt{3}i \] Then multiplying by 2: \[ 2 \sqrt{-75} = 2 \cdot 5\sqrt{3}i = 10\sqrt{3}i \] Next, for \( \sqrt{25} \): \[ \sqrt{25} = 5 \] Then multiplying by 8: \[ 8 \sqrt{25} = 8 \cdot 5 = 40 \] Now, putting it all together: \[ 2 \sqrt{-75} + 8 \sqrt{25} = 10\sqrt{3}i + 40 \] Thus, the result expressed as a simplified complex number is: \[ 40 + 10\sqrt{3}i \]