what is the square-root of, minus one ?

Answer 1

imaginary number

sqrt -1 = i

Answer 2

There is no real number solution to the sq.rt. of (-1). In every day parlance 'you can't have a square root of a negative number.'

But mathematicians find this very inconvenient. For example, some quadratic equations don't have a real number solution because it involves find the square root of a negative number.

So what is to be done? Simple, the 'answer' is invented! The square root of (-1) is i. This is written as:

sq.rt (-1) = i (except I can't type the proper sq.root sign!)

That now makes things easy because the sq.rt. (-25) is:

sq.rt. (25 x -1)

= sq.rt (25) x sq.rt (-1)

= 5 x sq.rt (-1)

= 5i

Since i is NOT a real number it, and numbers of the form ai, are called imaginary numbers.

Now, if you have say, 7 + ai, that's not a real number and it's not an imaginary number, it's a bit of both and is called a complex number.

Answer 3

1

Answer 4

The square root of minus one will be an imaginary number, i. You cannot take the square root of a negative number unless you are using the imaginary number, i.

Answer 5

Every number has two square-roots, three cube roots, four fourth-roots, etc. One of the square-roots of -1 is given the symbol i and the other is -i. Unlike for the ten base digits 0,1,2,3,....9, they didn't invent a unique symbol for this number.

The following source gives an excellent answer to your question. Its unbeatable. Just check out the first chapter. It helped change my entire outlook on Mathematics, a long time ago.

Answer 6

You cannot take the square root of a negative number.

However, we can arbitrarily define that there exists a number that when squared is -1.
Let:
i^2 = -1

From that follows that sqrt(i) = -1

It happens to be so that the introduction of this number not only makes life easier but opens up a whole new field of analysis, complex analysis.

Answer 7

1

Answer 8

In real numbers, it does not exist. There are no numbers (negative or positive) in a well-ordered field, that can be multiplied by themselves to yield a negative number.

So, someone "imagined" a number (called "i" or "j", depending on the book -- electrical engineers use "j" because they already use "i" for something else) such that when this number is multiplied by itself, the result is -1. It is an "imaginary" number.

A mathematical field constructed by mixing real numbers with this imaginary one, is called a complex field (and the numbers are called complex numbers).

In popular language, we say that i (or j) is the square root of -1. But in strict mathematical definitions, we don't. We say: " i is such that i squared is equal to -1 " without actually stating that it is a square root.

Answer 9

As far as ordinary, everyday numbers go, the square root of minus one does not exist*

Answer 10

You need to use complex numbers - so that 'j' or sometimes 'i' is the square root of minus one, thus: -

j * j = -1

or

i*i = -1

The choice of 'j' or 'i' depends upon your notation for the complex number system!

Answer 11

OK

Sqrt -1 = i

This is an imaginary number, signified by the symbol i.
And i*i or i^2 = -1.

Hope that helps.