Dividing complex numbers and making the denominator simpler might seem hard at first, but it's really not that bad! Let’s break it down step by step.

How to Divide Complex Numbers:

1. Know What Complex Numbers Are: You’re usually given two complex numbers, like $a + bi$. Here, $a$ and $b$ are regular numbers, and $i$ stands for the imaginary unit.

2. Write the Division: For example, if you want to divide $(3 + 2i)$ by $(1 - 4i)$, it looks like this: $\frac{3 + 2i}{1 - 4i}$

3. Use the Conjugate: To remove the imaginary part in the bottom number, you need to multiply both the top (numerator) and the bottom (denominator) by the conjugate of the denominator.

   For the denominator $1 - 4i$, the conjugate is $1 + 4i$. So, it looks like this: $\frac{(3 + 2i)(1 + 4i)}{(1 - 4i)(1 + 4i)}$

4. Do the Multiplication: Now, multiply everything out for both the top and the bottom. Be careful when you distribute and combine similar terms!

5. Simplify the Result: After you’ve multiplied, combine any similar terms and simplify everything. If you have a mix of real and imaginary numbers, separate them.

6. Final Answer: The answer should be in the form $a + bi$. Just like that, you’ve made the denominator simpler!

It might take some practice, but you’ll get the hang of it!