# A Visual, Intuitive Guide to Imaginary Numbers

Learn to understand i, the imaginary number, as a rotation. Full article:...

45K views betterexplained.com## Interest

on Dec 21, 2007

# Stumblers Who Commented On This Page

## classof1

### Classof1

excellent explanation, good job

## rhlvora

### Rahul

This is amazing.

## stereotomy

### Cagrie Arase

imaginary numbers... AGAIN!

## Janopus

### Jan

hHmmm ... i spotted this site from Awils' (a precocious young woman) links (http://awils1.stumbleupon.com/review/27910945/); but I see a number of friends have been here. I just wanted to point out that there is a wonderful book on the history of the square root of -1 by Paul Nahin, a professor of electrical engineering at U. of New Hampshire. Here is the link: http://press.princeton.edu/titles/6388.html. I have always been fascinated by (-1)^1/2, but I never had a deep understanding. Prof. Nahin does. It crops up throughout science and a has been a frustration for me, especially in the theory of NMR spectroscopy where e^i*omega*t describes the periodic precession of nuclear spins in a magnetic field. I more or less get it now. Also, there that most amazing equation in all of mathematics e^i*pi = -1. There is an only joke: A mathematician is a person to whom it is obvious that exp(-i*pi) = -1. Fascinating. Maybe in my next life time. Did I get the minus sign right? duh.... jano

http://www.futilitycloset.com/2007/07/15/eulers-identity/

## mrcclass

### mrcclass

I am just finding out about this website which tries to explain math ideas in different ways. What we have here is an entertaining approach to something as simple as negative numbers- it gives the history of them, the intuitive meaning of them- and soooo much more. Yes, you are afraid of mathematics but no one is watching you stumble this page, so go look. And if someone is watching you, it will make you look smart.

With thanks to the always fine stumblers awils.stumbleupon.com and M-104.stumbleupon.com.

## Awils1

### Amy

Thanks to M-104; this is further proof that the constant expansion of high-school curricula should not be supported. Details as to the how, why, and when make all the difference in understanding mathematics, and such squished curricula leave no room for such detail.

## M-104

### Kazuo

BetterExplained delivers again with another helpful guide to developing some visual intuition for an otherwise "strange" mathematical concept. Imaginary numbers are quite important, and my eyebrows went up a bit when the article mentioned that the graphical interpretation wasn't hit upon until decades after first invention of the idea.

## ggishh

### ggishh

A sometimes initially difficult subject matter explained very well for those of us who don't instantly grasp complex numbers.

## cjlowe

## Chris

It's good, but I once had to explain imaginary numbers in a way a non-mathematically minded person would understand. I put it like this:

"What is 1x1"

"1"

"What is negative 1 x negative 1"

"1"

"So what number multiplied by itself equals 1"

"1"

"and what else?"

"-1"

"Good. So what number multiplied by itself equals -1"

"There is no answer"

"No that's not true. The answer is an imaginary number"