Students will learn why the following properties are true $$z + \overline{z} = 2\operatorname{Re}(z)$$ $$z \cdot \overline{z} = \lvert z \rvert^2$$
Watch this for an introduction to complex conjugates, and proof of the two aforementioned properties. Here's a video on how to find the complex conjugate given a complex number.
Conclude by giving your students these challenges:
- Ladybird Count by NRICH
- Octa Space by NRICH
- 1999 AMC 8, Problem 15
- Pierce Book Fair by Pierce School: Problem / Solution