Understanding Complex Numbers

What are Complex Numbers?
Complex numbers are written as $a + bi$. Here, $a$ is called the real part, and $b$ is the imaginary part. The letter $i$ stands for the square root of -1.

Why Do They Matter?
About 15% of questions on Algebra II tests are about complex numbers. So, knowing how to work with them is important!

How to Divide Complex Numbers

1. Use the Conjugate:
   To divide complex numbers, you first multiply both the top and bottom by the conjugate of the bottom.

The conjugate of a number like $c + di$ is $c - di$.

Example:
If you want to divide:

$$\frac{a + bi}{c + di}$$

You multiply it like this:

$$\frac{a + bi}{c + di} \times \frac{c - di}{c - di}$$

2. Simplifying the Expression:
   After you change the fractions, use the distributive property, also known as the FOIL method, to make it simpler.

For example:

$$(a + bi)(c - di) = ac + adi - bci - bdi^2$$

Practice Makes Perfect

• Practice Problems: Doing regular practice will help you get better. Try to solve at least 5-10 problems every day to become skilled.

• Online Resources: Websites like Khan Academy and Coursera have many lessons on complex numbers. There are even over 100 videos just for this topic!

Stay Committed

• Make It a Habit: Try to study a little bit every day. Research shows that students who practice regularly can improve by up to 25% on tests about complex numbers.

By using these methods, you can get better at dividing complex numbers and improve your overall algebra skills!