Chapter A.7, Problem 28AYU

To determine

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

Answer to Problem 28AYU

The given expression in the standard form $a+ib$ is $-\frac{1}{2}+\frac{5}{2}i$ .

Explanation of Solution

Given information:

The expression is $\frac{2+3i}{1-i}$ .

Calculation:

Consider the expression.

  $\begin{array}{c}\frac{2+3i}{1-i}=\frac{2+3i}{1-i}\frac{\left(1+i\right)}{\left(1+i\right)}\\ =\frac{2+2i+3i+3\left(-1\right)}{1-\left(-1\right)}\\ =\frac{-1+5i}{2}\\ =-\frac{1}{2}+\frac{5}{2}i\end{array}$