Chapter A.7, Problem 27AYU

To determine

To write:The given expression in the standard form $a+ib$ .

Answer to Problem 27AYU

The given expression in the standard form $a+ib$ is $\frac{5}{2}-\frac{7}{2}i$ .

Explanation of Solution

Given information:

The expression is $\frac{6-i}{1+i}$ .

Calculation:

Consider the expression.

  $\begin{array}{c}\frac{6-i}{1+i}=\frac{6-i}{1+i}\frac{\left(1-i\right)}{\left(1-i\right)}\\ =\frac{6-6i-i+\left(-1\right)}{1-\left(-1\right)}\\ =\frac{5-7i}{2}\\ =\frac{5}{2}-\frac{7}{2}i\end{array}$