The imaginary unit, called $i$, is really important for understanding complex numbers. It helps us solve equations that don’t have real answers, like $x^2 + 1 = 0$.

In this case, we find out that $i^2 = -1$. This gives us a brand new way to think about numbers!

Properties of $i$:

1. $i^1 = i$ (Just $i$)
2. $i^2 = -1$ (This is a big one!)
3. $i^3 = -i$
4. $i^4 = 1$ (And then it starts over!)

Since these rules repeat, they make complex math easier.

With $i$, we can write complex numbers in a simple way, like $a + bi$. This helps us work with these numbers in different math problems!