Simplify the expression to \( a+b i \) form: \[ \sqrt{100}-\sqrt{-7}+\sqrt{36}-\sqrt{-63} \]

To simplify the expression \( \sqrt{100} - \sqrt{-7} + \sqrt{36} - \sqrt{-63} \), we first handle each term separately. 1. \( \sqrt{100} = 10 \) 2. \( \sqrt{-7} = \sqrt{7} i \) (since \( \sqrt{-1} = i \)) 3. \( \sqrt{36} = 6 \) 4. \( \sqrt{-63} = \sqrt{63} i = \sqrt{9 \cdot 7} i = 3\sqrt{7} i \) Now, substituting these values back into the expression gives: \[ 10 - \sqrt{7} i + 6 - 3\sqrt{7} i \] Next, combine the real parts and the imaginary parts: - Real part: \( 10 + 6 = 16 \) - Imaginary part: \( -\sqrt{7} i - 3\sqrt{7} i = (-1 - 3)\sqrt{7} i = -4\sqrt{7} i \) Putting it all together, we have: \[ 16 - 4\sqrt{7} i \] Thus, the simplified expression in the form \( a + bi \) is: \[ 16 - 4\sqrt{7} i \]