Happy Wednesday and back to school season math friends! This post introduces imaginary and complex numbers when raised to any power exponent and when multiplied together as a binomial. When it comes to all types of learners, we got you between the video, blog post, and practice problems below. Happy calculating! ðŸ™‚

**What are Imaginary Numbers?**

Imaginary numbers happen when there is a negative under a radical and looks something like this:

**Why does this work?**

In math, we cannot have a negative under a radical because the number under the square root represents a number times itself, which will always give us a positive number.

**Example**:

**But wait, thereâ€™s more:**

When raised to a power, imaginary numbers can have the following different values:

Knowing these rules, we can evaluate imaginary numbers, that are raised to any value exponent! Take a look below:

-> We use long division, and divide our exponent value 54, by 4.

-> Now take the value of the remainder, which is 2, and replace our original exponent. Then evaluate the new value of the exponent based on our rules.

**What are Complex Numbers?**

Complex numbers combine imaginary numbers and real numbers within one expression in a+bi form. For example, (3+2i) is a complex number. Letâ€™s evaluate a binomial multiplying two complex numbers together and see what happens:

-> There are several ways to multiply these complex numbers together. To make it easy, Iâ€™m going to show the Box method below:

Try mastering imaginary and complex numbers on your own with the questions below!

**Practice:**

**Solutions:**

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! ðŸ™‚