Complex numbers and complex questions!

Whats square root of -1?

Even if u had basic maths in school , you will realise that its i(defined as square root of negative).

Big deal..I have been dealin with this for almost half of my life (being an electrical engineer..i is impossible to escape)

But then sometimes I think its fine..but what does i mean in "reality". There are thousands of definations... i is the part of y axis of argand diagram...i means an operation of 90 degree rotation..etc etc..

but just think about this..

i= sqrt(-1)

lets  define all this in "reality"

1= as in one ness..one apple , two apple..etc

sqrt= operation defining a number multiplied by the same (inverse)

-     = subtract(take away)

now what does i represent?

  

where is i in the "real world"?

1 is there, sqrt is there, subtract is there....but where the f$%% is i?

first of all is "i" allowed in real numbers? what is it ?

I think i know the answer..or maybe its a guess..

There is no "i" in the real world ..because there is no number in the "real world". When I say that What I mean is that we may relate numbers to "one ness".."twoness" ..etc but they are just equivalences . One apple is equivalent to one orange ..but only when we imagine it to be so.

In that case the number one is imaginary. So is the operation sqrt and hence "i" is also imaginary. Its not different from 1,2,3...

Even operations like "additions" and sunbtractions are imaginary..

Let me explain..Suppose you say  1+1=2

    I may ask you what does it mean in real world. ..? You might say that one banana and one banana makes 2 bananas. But look at this closely...What you have defined is a "rule" that you have empirically made. Its not a fundamental property of the "number"...

How do you know that after adding a million pair of bananas you might not get 1+1=1.5?

Hence is there any point relating numbers and mathematics to the real world?

A straight line is abstract and at most is a model. That it fits most observations is only a coincindence. How do we know for sure that a more fundamental shape doesnt exist?

Which brings me to the dilema that I found perplexing in school...

Why do teachers try to relate maths as a real life example? Isnt it factually and conceptually wrong? Isnt it wrong to teach that 1+1=2 because one banana plus one banana is equal to two bananas?

Isnt it better we just say that in our game called mathematics..these are symbols 1 and "+" is a operator. Lets define rules and play the game...

The game may be close to real life but its not real life...Not in all situations in real life will 1+1=2