enough about the conjectural nature of infinity-does the sqrt of -1 really exist? if so prove it?

Answer 1

√(-1) 'exists' in the same sense as √2 or π 'exist'. That is to say, they exist by definition.

But they're pretty useful definitions.

BTW, next time go for something deep. For example: Show me the concept of 'five' without making reference to a collection of five objects. I want to see 'fiveness' all by itself, not in terms of anything else ☺


Doug

Answer 2

The square root of -1 does not 'exist' - that's why it is called an imaginary number!

'i' is simply a mathematical shorthand which means "the number, that if it existed, would be equal to the square root of minus 1"

Then once you have i, you can do all sorts of useful, exciting and fun things with it*... but only in your head or on paper. You are never going to see 5i ducks in a pond.

*exciting and fun to a mathematician, anyway

Answer 3

Existence is a property of physical objects like dogs, cats, and the ink (or phosphorescent pattern) you draw numbers with. The numbers themselves are abstractions only - ideas, with rules of inference. Think of them as objects in a game. Does the game of chess exist anywhere? Not the pieces and board. That's like the ink of numbers. I mean the game itself. All numbers are imaginary by the more common definition of the word. They are useful for counting our possessions and designing airplanes. i=sqrt -1 is used in a game where i X i = -1 is a move. That is all.

Answer 4

yes....it exists in the same way that pi and infinity exist.....it is called j and it is used in mathematics a lot (j notation) it is known as an imaginary number.
It is useful in working out phases, sine and cosine waves for electromagentic (radio) propogation.

If you are talking about 'really exist' as in something you can carve into a piece of wood, then the answer would be No

Answer 5

The square root of -1 exists.
Infinity and infinite exist.

Intangible - but if it didn't exist, you wouldn't have been able to ask your question.

The problem arises only when the status of its existance is confused with reality.

Answer 6

In engineering terms i squared equals -1
therefore sqrt of -1 = i
This helps in setting up real and imaginery planes on axis
If you want to know more look in maths books for imaginery numbers / fields.