Science:Math Exam Resources/Courses/MATH152/April 2022/Question A03/Solution 2

Providing an alternate way to simplify the second complex number. Looking at the denominator, we can see that multiplying by ${\textstyle 1+i}$ will get rid of the imaginary value,

$${\begin{aligned}{\frac {(1-3i)(1+i)}{(1-i)(1+i)}}&={\frac {4-2i}{2}}\\&=2-i.\end{aligned}}$$