\( 1 \& \) Find the following product and write the result in standard form, \( a+b i \) \[ (-5+i)(3+i) \] \( (-5+i)(3+i)=\square \)

To find the product \( (-5+i)(3+i) \), we can use the distributive property (also known as the FOIL method for binomials): \[ (-5)(3) + (-5)(i) + (i)(3) + (i)(i) \] Calculating each term, we get: - \( -5 \times 3 = -15 \) - \( -5 \times i = -5i \) - \( i \times 3 = 3i \) - \( i \times i = i^2 = -1 \) Now, combine all these results: \[ -15 - 5i + 3i - 1 \] Combine the real parts and the imaginary parts: \[ (-15 - 1) + (-5i + 3i) = -16 - 2i \] So, the result in standard form \( a + bi \) is: \[ (-5+i)(3+i) = -16 - 2i \]