Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 111: 29

$\displaystyle\frac{5}{2}-\frac{7}{2}i$

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain: $\displaystyle \frac{6-i}{1+i}$ $\displaystyle=\frac{6-i}{1+i}*\frac{1-i}{1-i}$ $\displaystyle=\frac{6-6i-i+i^{2}}{1-i+i-i^{2}}$ $\displaystyle=\frac{6-7i+-1}{1--1}$ $\displaystyle=\frac{5-7i}{2}$ $\displaystyle=\frac{5}{2}-\frac{7}{2}i$