So! Today's lesson is about complex numbers and complex conjugation!
The complex numbers start off rather simple by accepting that the numbers i and -i are solutions to the equation x^2 = -1
This makes for some pretty handy math!
Let's take an example:
We have the complex number z = 2 - 3i, and its complex conjugated counterpart: w = 2 + 3i.
What happens when we multiply these with each other?
z*w = (2 - 3i) * (2 + 3i) = 2 * (2 - 3i) + 3i * (2 - 3i) = 4 - 6i + 6i - 9 i^2 = 4 - 9 * (-1) = 4 + 9 = 13.
There! Have fun!