Add and simplify. \[ (8+8 i)+(4-7 i) \]

Step 1 ：We are given two complex numbers, \(8+8i\) and \(4-7i\).

Step 2 ：To add these two complex numbers, we add the real parts together and the imaginary parts together separately.

Step 3 ：The real parts are 8 and 4, and the imaginary parts are 8i and -7i.

Step 4 ：Adding the real parts, 8 and 4, gives us 12.

Step 5 ：Adding the imaginary parts, 8i and -7i, gives us i.

Step 6 ：So, the sum of the two complex numbers is \(12 + i\).

Step 7 ：Final Answer: The sum of the two complex numbers is \(\boxed{12 + i}\).