Step 1 :Given the expression \((2+\sqrt{-16})+(6+\sqrt{-49})\).
Step 2 :Recall that the square root of a negative number can be expressed as a multiple of \(i\), where \(i\) is the imaginary unit with the property that \(i^2 = -1\).
Step 3 :So, \(\sqrt{-16} = 4i\) and \(\sqrt{-49} = 7i\).
Step 4 :Substitute these values back into the expression to get \((2+4i)+(6+7i)\).
Step 5 :Add the real parts together and the imaginary parts together separately to get \(8+11i\).
Step 6 :Final Answer: The simplified form of the given expression is \(\boxed{8+11i}\).