# BLOGS WEBSITE

# TAG: iplanes

#### Where the complex points are: i-arrows

Problems with i-planes

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 […]

#### Where the complex points are: on a real circle

Introduction

In 2016 I created the iplane idea, which allows you to locate the complex points on a real graph.

In case you haven’t heard of it or you need reminding, the idea is that at every real point (p,q) of the real plane, there is a planes-worth of complex points attached, all of which have coordinates […]

#### Return to the iplane: A complex line

It’s been four years since I came up with the idea of iplanes as a way to organise the complex points on a graph, and in the intervening time I have thought about them on and off. For some reason right now I am thinking about them a lot, and I thought I would write […]

#### Where the complex points are: where the idea came from

This is the last (for now) in a series of posts about Where the Complex Points Are. To catch you up, I discovered a way of visualising where the complex points are in relation to the points of the real plane. All the complex points (p+ri,q+si) are in a plane attached to the real plane […]

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#### Where the complex points are: the graph of a function

This is the fourth in a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line

Where the complex points are: on a parabola

Where the complex points are: the graph of a function (YOU ARE HERE)

Where the complex points are: where the idea […]

3 Comments

#### Where the complex points are: on a parabola

This is the third in what has turned out to be a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line

Where the complex points are: on a parabola (YOU ARE HERE)

Where the complex points are: the graph of a function

Where the […]

2 Comments

#### Where the complex points are: on a line

This is the second in what has turned out to be a series on Where the Complex Points Are.

Where the complex points are: introduction to the iplane concept

Where the complex points are: on a line (YOU ARE HERE)

Where the complex points are: on a parabola

Where the complex points are: the graph of a function

Where the […]

3 Comments

#### Where the complex points are

When you first learn complex numbers, you find out that they give you ways to solve equations that were previously unsolvable. The classic example is the equation equation x^2 + 1 = 0, which if you’re only using real numbers has no solutions, but with complex numbers has the solutions x=i and x=-i.

As someone who […]

10 Comments