1. what is complex number? (a pair of real numbers, put together, that you can multiply together)

2. why we need it? (I will leave that to you)

3. how to think about it? (Cartesian coordinate, polar coordinate. )

4. what can you do with it? (multiplication, addition.)

5. real part, imaginary part, modulus (absolute value), argument (aka phase angle)

6. complex conjugate. (hey, what does $\sqrt{-1}$ mean? $i$ or $-i$? does it matter? do we have a preference?)

(optional) other weird “numbers”? (if you walk like a number, talk like a number, operate like a number, I will call you a number!) The notion of a 'field'.