Where the complex points are: i-arrows

Once upon a time in 2016, I created the idea of iplanes, which I consider to be one of my biggest maths ideas of all time. It was a way of me visualising where the complex points are on the graph of a real function while still being able to see the original graph. But there was a problem with it: the thing I want, which is to see where the complex points are (or at least look like they are) is several steps away from locating them.

However, in my original series of blog posts, I actually already created a solution to this problem! I can draw a complex number as an arrow on the real line, which starts at the real part and extends in the length and direction of the imaginary part. Anyway, combining this arrow model of a complex number from an x-coordinate and a y-coordinate produces an arrow in the plane. The point (p+si,q+ti) is an arrow based at the point (p,q) and extending along the journey (s,t) from there. 

This is the representation I need. I have decided to call them i-arrows.

You can read the rest of this blog post, and all eight blog posts in the i-arrows series, in PDF form here.

The titles of the eight posts in the series are:

1. Where the complex points are: i-arrows
2. The complex points on a line using i-arrows
3. Further updates on the complex points on an unreal line using i-arrows
4. The complex points on a line in finite geometry using i-arrows
5. The complex points on a parabola using i-arrows
6. The complex points on real circles using i-arrows
7. The complex points on unreal circles using i-arrows
8. The line joining two complex points using i-arrows