This task comes in two parts.

The first is a sequence of questions where pupils have to convert complex numbers to polar form. The table layout serves as a scaffold for their thinking during this process. The inclusion of the “principle argument” column is due to my experience of pupils forgetting to adjust their angle to be in the correct range of values.

The second task is more demanding. The hardest element is likely converting back to the z = a + ib representation. I know I found it tough to create questions for this part.

It’s hard to come up with a modulus which has an obvious a and b value associated, which also comes out with a nice exact value for the argument. One runs out of nice examples quite quickly. That’s why I ended up including some non-exact radian values too.

It’s all about trig and Pythagoras interacting and restricting each other. Fascinating stuff, which has given me an idea for a task for much younger pupils…

Credit: @chrismcgrane84