Add and simplify.
\[
(2+\sqrt{-16})+(6+\sqrt{-49})
\]
\[
(2+\sqrt{-16})+(6+\sqrt{-49})=\square
\]
(Simplify your answer. Type your answer in the form $a+b i$.)
Answer
Final Answer: The simplified form of the given expression is \(\boxed{8+11i}\).
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 \(\boxed{8+11i}\).
