# 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**.

The titles of the eight posts in the series are:

- Where the complex points are: i-arrows
- The complex points on a line using i-arrows
- Further updates on the complex points on an unreal line using i-arrows
- The complex points on a line in finite geometry using i-arrows
- The complex points on a parabola using i-arrows
- The complex points on real circles using i-arrows
- The complex points on unreal circles using i-arrows
- The line joining two complex points using i-arrows