When students switch between two ways of writing complex numbers, they often run into some common problems. These problems can make it hard for them to really understand the topic.

Let’s look at these mistakes:

1. Wrong Calculation of $r$:
   Sometimes, students forget how to find $r$. The formula is $r = \sqrt{a^2 + b^2}$. If they skip squaring both $a$ and $b$, they can get the wrong answer.

2. Miscalculating $\theta$:
   Getting the angle $\theta$ right is super important. Many students forget to check which quadrant they are in. This can lead them to a wrong answer. They need to remember that $\tan \theta = \frac{b}{a}$, but they should be careful about the signs of $a$ and $b$.

3. Forgetting to Simplify:
   After changing the form, it’s important to keep the simplest version. Sometimes, students don’t notice things that can make the expression easier.

To avoid these mistakes, practicing with clear steps and checking their work can help students feel more sure about switching between these two forms.