\( \left. \begin{array} { | l | } \hline \text { Operations on Complex Numbers } \\ \hline \text { Simplify each of the following and write in the form a + bi. } \\ \hline ( 8 + 6 i ) - ( 9 + 3 i ) = \\ \hline ( 11 - i ) ( 15 + i ) = \\ \hline \end{array} \right. \)

To simplify \( ( 8 + 6 i ) - ( 9 + 3 i ) \), we subtract the real parts and the imaginary parts separately. So, \( 8 - 9 = -1 \) and \( 6 i - 3 i = 3 i \). This gives us the result \( -1 + 3i \). For \( ( 11 - i ) ( 15 + i ) \), we use the distributive property (FOIL). First: \( 11 \times 15 = 165 \). Outer: \( 11 \times i = 11i \). Inner: \( -i \times 15 = -15i \). Last: \( -i \times i = -i^2 = 1 \) (since \( i^2 = -1 \)). Now, combine: \( 165 + 1 + (11i - 15i) = 166 - 4i \). So the results are: \( ( 8 + 6 i ) - ( 9 + 3 i ) = -1 + 3i \) \( ( 11 - i ) ( 15 + i ) = 166 - 4i \)