The imaginary unit, called $i$, has some cool features that help us understand complex numbers.

Let’s break it down:

• What is $i$?
  $i$ is known as the square root of $-1$. This means that when you multiply $i$ by itself, you get $-1$. So, we can say $i^2 = -1$.

• Powers of $i$:
  As you work with $i$, it helps to know what happens when you raise it to higher powers:

  • For $i^3$, you can think of it like this:
    $i^3 = i \cdot i^2 = i \cdot (-1) = -i$.

  • For $i^4$, it’s easier:
    $i^4 = (i^2)^2 = (-1)^2 = 1$.

You'll notice that the powers of $i$ repeat every four steps. This pattern makes doing calculations with $i$ much simpler once you see it!