When you work with complex numbers, avoiding common mistakes can help you save time and avoid confusion. Here are some things to keep in mind:

1. Correct Format: Always write complex numbers like this: $a + bi$. For example, $3 + 4i$ is right, but $3, 4i$ is not.

2. Remember to Distribute: When you multiply, make sure to distribute correctly. For example, if you’re multiplying $(1 + 2i)(3 + 4i)$, use the distributive property like this:

   $(1 \cdot 3) + (1 \cdot 4i) + (2i \cdot 3) + (2i \cdot 4i) = 3 + 4i + 6i - 8 = -5 + 10i.$

3. Using Conjugates: When you divide complex numbers, you need to multiply by the conjugate. For example, if you are dividing $\frac{2 + 3i}{1 - 2i}$, multiply both the top (numerator) and the bottom (denominator) by $(1 + 2i)$ to get rid of the imaginary part in the bottom.

By paying attention to these details, your work with complex numbers will be much easier!