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

To simplify the expression \((2 + i)(8 + 6i)\), we'll use the distributive property (also known as the FOIL method for multiplying binomials): \[ (2 + i)(8 + 6i) = 2 \cdot 8 + 2 \cdot 6i + i \cdot 8 + i \cdot 6i \] Let's calculate each term: 1. **First terms:** \(2 \cdot 8 = 16\) 2. **Outer terms:** \(2 \cdot 6i = 12i\) 3. **Inner terms:** \(i \cdot 8 = 8i\) 4. **Last terms:** \(i \cdot 6i = 6i^2\) Now, combine these results: \[ 16 + 12i + 8i + 6i^2 \] Since \(i^2 = -1\), substitute: \[ 16 + 20i + 6(-1) = 16 + 20i - 6 = 10 + 20i \] So, the simplified form of the expression is: \[ 10 + 20i \] **Final Answer:** \[\boxed{10 + 20i}\]