What is the square root of minus 1?

**Colin Manson** · 14-Sep-06, 17:29

The answer is i

http://en.wikipedia.org/wiki/Imaginary_unit

**jimag** · 14-Sep-06, 18:51

i but it was j when i was young

**Colin Manson** · 14-Sep-06, 19:25

Alternative notation

In electrical engineering and related fields, the imaginary unit is often written as j to avoid confusion with electrical current as a function of time, traditionally denoted by i(t) or just i. The Python programming language also uses j to denote the imaginary unit.

**kenimac1** · 14-Sep-06, 19:34

I think that using a complicated form of differentiation you could calculate a theoretical answer........
but in practical terms you can't have a square root for a negative number.

**porshiepoo** · 14-Sep-06, 19:44

Originally Posted by kenimac1

I think that using a complicated form of differentiation you could calculate a theoretical answer........
but in practical terms you can't have a square root for a negative number.

Think you can now! Wasn't the i invented (or whatever) so that you could find and use the square root of an negative number? It was then termed an 'imaginary' number hence the 'i'? Or have I gone all thick again???

**canuck** · 14-Sep-06, 20:45

Where is our white knight when we need him to come charging in and explain all of this to us. DrSzin stop trying on kilts and get over here before our brains explode.

**futurelegends** · 14-Sep-06, 21:24

I'm sure when I was at College it was -j , so I'll say -i.

**Sporran** · 14-Sep-06, 21:36

Originally Posted by canuck

Where is our white knight when we need him to come charging in and explain all of this to us. DrSzin stop trying on kilts and get over here before our brains explode.

The good doc is certainly conspicuous by his absence! Perhaps he's away at some exotic location for the Szin in Kilts photo shoot!

**DrSzin** · 15-Sep-06, 00:16

I didn't think my input was needed.

Porshiepoo gave the answer, explained why there are two roots, and explained why imaginary numbers are needed. Meanwhile, Colin's link to the Wikipedia page provided enough detail to sink a battleship in dihydrogen monoxide.

As Wikipedia explains in detail, there are two solutions to the equation

,

and these values for x, namely x = i and x = -i, are called the roots of the equation. The imaginary number i is defined by its square, namely i x i = -1. By convention, i (as opposed to -i) is usually called the square root of -1. Similarly, we usually say that 2 (as opposed to -2) is the square root of 4.

If I were marking an exam I would give full marks to the last and third-last answers, but take one mark off for the second-last one - for being obtuse! The answer "it doesn't exist" is ok if you restrict your answer to the set of real numbers.

There's a reasonable introduction to complex numbers on this Wikipedia page, but it gets hard quite quickly.

Originally Posted by Colin Manson

Alternative notation

In electrical engineering and related fields, the imaginary unit is often written as j to avoid confusion with electrical current as a function of time, traditionally denoted by i(t) or just i.

Yup, and vice versa for physicists. We usually use i for the square root of -1, and j for the current density (the charge passing through unit area per unit time.)

**mostlyharmless** · 15-Sep-06, 00:23

Imaginary Numbers grievous....

I doubt I will ever encounter a situation where I will have to deal with square roots of negative numbers. How can it be done ? After all, a positive number squared or a negative number squared will always equal a positive number?!

Mathematicians[how clever] have designated a special number 'i' which is equal to the square root of minus 1. Then, it follows that i2 = -1. To determine the square root of a negative number (-16 for example), take the square root of the absolute value of the number (square root of 16 = 4) and then multiply it by 'i'. So, the square root of -16 is 4i.
As a double check, we can square 4i (4*4 = 16 and i*i =-1), producing -16.
All negative square roots are called "imaginary numbers" (now you know where that letter 'i' comes from)........great!

**KitKat** · 15-Sep-06, 02:43

well THAT cured my insomnia!!

**Saveman** · 15-Sep-06, 08:31

So we've got the answer then: i.....an imaginary number.

I suppose -1 is imaginary anyway because how can you have -1 apples? If you've got -1 apples you might as well have -7654 apples......it'll not make a lot of difference.

What I want to know is......how many "i"s does it take to change a lightbulb?