Complex affine space

Okay, kiddo, let's start with something you might be familiar with - a simple boy or girl who lives in a house. We can label different parts of the house, like the bedroom, kitchen, and living room, with coordinates to help us find things easily.

Now, let's imagine a bigger space where all kinds of objects exist. This space is called an affine space. It's like a big playground where different things - like points, lines, and shapes - can move around and play together.

In a complex affine space, everything is a bit more complicated because the coordinates are made up of complex numbers instead of just simple numbers. Complex numbers are like two numbers put together - a real number and an imaginary number. Imagine putting two puzzle pieces together to make a new piece that's a bit more complicated. That's what a complex number is like!

So, when we label things in a complex affine space with coordinates, we have to use pairs of complex numbers to describe exactly where something is located.

Overall, complex affine spaces might seem a bit daunting at first, but they just involve more complex numbers and coordinates to describe where things are. And just like on the playground, everything can still play nicely together as long as we use the right information to keep track of everything!