Add or subtract as indicated. Express your answer in standard form. \( (-6-\sqrt{-18})+(-4+\sqrt{-72}) \)

To solve the expression \( (-6-\sqrt{-18})+(-4+\sqrt{-72}) \), we first simplify the square root terms. The term \( \sqrt{-18} \) can be simplified as follows: \[ \sqrt{-18} = \sqrt{18} \cdot i = \sqrt{9 \cdot 2} \cdot i = 3\sqrt{2} \cdot i \] Next, we simplify \( \sqrt{-72} \): \[ \sqrt{-72} = \sqrt{72} \cdot i = \sqrt{36 \cdot 2} \cdot i = 6\sqrt{2} \cdot i \] Now, substituting these back into the expression: \[ (-6 - 3\sqrt{2}i) + (-4 + 6\sqrt{2}i) \] Next, we combine like terms: - The real parts: \(-6 - 4 = -10\) - The imaginary parts: \(-3\sqrt{2}i + 6\sqrt{2}i = 3\sqrt{2}i\) Thus, our final expression is: \[ -10 + 3\sqrt{2}i \] Expressed in standard form, the answer is: \[ \boxed{-10 + 3\sqrt{2}i} \]