## A Conversation for Imaginary Numbers

### Help!

Modo Started conversation Mar 19, 2001

I love science, especially physics, and I want to learn as much as I can about it. But math is not my strong suit. I'm in my first year of college and I'm still grappling with the concept of imaginary number (and a few other daunting concepts).

My question is this, how do imaginary numbers apply to concepts in physics; where do they arise, and for what reasons?

### Help!

Pablo Posted May 15, 2001

Im not an expert, but i have encountered imaginary numbers in Physics, in particular, electronics, plasma-physics & laser-physics (attenuated signals).

As i said, im not a maths expert, but as far as i know, we use imaginary numbers as a tool to simplify, Eg we transform an equation to the complex plane, mess arund with it untill it is in a form we require, then transform back to gain the answer.

A common usage is to express exp(it)=cos(t)+isin(t) where t=theta. This enables you to simplify algebra envolving lots of sin's and cos's quite conveiniently.

This is not the full extent of its use but all that i can remember!

### Help!

DZ Posted Jul 17, 2001

Imaginary numbers crop up all the time in physics - you''l come across them soon enough! Rest assured, even though they seem strange now, they'll become second nature soon enough.

As the pevious poster said, one of the first places imaginary numbers crop up is dealing with sine and cosine. These can be rewritten in terms of exp(i * theta). Doing this makes a lot of maths easier, and means that many of those tedious trig identities you are supposed to memorize become obvious. Using this form of sin and cosine makes all problems involving them a lot more simple, such as in AC circuits, interference of waves, even in understanding relativity etc. etc.

A little bit of effort in 'inventing' these numbers makes a lot of calculations a lot easier. As well as this though, there are some things that only complex numbers can describe. The most famous fractal, the mandlebrot set, using complex numbers, as do many others.

Also, the equations of quantum mechanics rely on complex numbers and could not be described without them - so some of the most fundamental aspects of physics need imaginary numbers to work.

After a few more years doing physics you'll soon think of them as just as real as other numbers and forget that you ever thought of them as 'imaginary'!

### Help!

DZ Posted Jul 17, 2001

Imaginary numbers crop up all the time in physics - you''l come across them soon enough! Rest assured, even though they seem strange now, they'll become second nature soon enough.

As the pevious poster said, one of the first places imaginary numbers crop up is dealing with sine and cosine. These can be rewritten in terms of exp(i * theta). Doing this makes a lot of maths easier, and means that many of those tedious trig identities you are supposed to memorize become obvious. Using this form of sin and cosine makes all problems involving them a lot more simple, such as in AC circuits, interference of waves, even in understanding relativity etc. etc.

A little bit of effort in 'inventing' these numbers makes a lot of calculations a lot easier. As well as this though, there are some things that only complex numbers can describe. The most famous fractal, the mandlebrot set, using complex numbers, as do many others.

Also, the equations of quantum mechanics rely on complex numbers and could not be described without them - so some of the most fundamental aspects of physics need imaginary numbers to work.

After a few more years doing physics you'll soon think of them as just as real as other numbers and forget that you ever thought of them as 'imaginary'!

### Help!

Apollyon - Grammar Fascist Posted Jun 29, 2004

In Ireland, we learn about Im numbers in the second half of secondary school. A couple of things:

1: It is not actually i, it is the Greek letter iota, probably chosen because iota is also used to express incredbily small amounts.

2: De Moivre's Theorem: e^i*k*A=(cosA + i*sinA)^k=conkA+i*sinkA. the original used n for k and theta for A, but I can't type theta and using k for n makes it easier to discern.

### Help!

Cefpret Posted Jun 29, 2004

I don't know much about the origin of "i", but today it's definitely "i" (or "j" for electrical engineers) and not iota.

And, this is not De Moivre's Theorem, but Euler's.

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