This task is intended as a lead in to the multiplication of complex numbers in polar form.  Some pupils may make the connection automatically, others may need some prompting to notice what is happening.  Experience of using the task has suggested it helps learners to develop their appreciation of the equivalence of the two representations of complex numbers, and also have a sense of the graphical interpretations.  Further, for those learners who do not make the conceptual leaps of their own accord, the exercise is still worth while practice.  

Credit:  @chrismcgrane84