Simplify the expression \[ (2+i)(8+6 i) \]

To simplify the expression \((2+i)(8+6i)\), we can use the distributive property (also known as the FOIL method for binomials): \[ (2+i)(8+6i) = 2 \cdot 8 + 2 \cdot 6i + i \cdot 8 + i \cdot 6i \] Calculating each term: 1. \(2 \cdot 8 = 16\) 2. \(2 \cdot 6i = 12i\) 3. \(i \cdot 8 = 8i\) 4. \(i \cdot 6i = 6i^2\) Now, recall that \(i^2 = -1\). Therefore, \(6i^2 = 6(-1) = -6\). Now, combine all the terms together: \[ 16 + 12i + 8i - 6 \] Combine the real parts and the imaginary parts: \[ (16 - 6) + (12i + 8i) = 10 + 20i \] Thus, the simplified expression is: \[ \boxed{10 + 20i} \]