Question

can any body explain me about iota

Answer 1

it is the ninth letter in the greek alphabet (translated to 'i').

it can also mean an extremly small amount.

Answer 2

See, when we are dealing with Square root, then you must know that square root of negative values is not defined, so to represent those terms, we introduced iota which is also basis of Complex Numbers../

Answer 3

You know about Number Sets, we have Natural Numbers Set, Whole Number Sets, Integers Set, Rational And Irrational Sets and above all Real Numbers Set..

But these real number set does not explain or include negative numbers under square root..

For example : \(\sqrt{4}\ = \pm 2\) is well defined and comes in Real Number Set..

But on the other hand:

\(\sqrt{-4}\) is not defined in real number set, so we use another set called Complex Number Set which includes both real as well as imaginary parts..

A complex number can be represented as: \(z = a+ ib\) where this \(i\) is called iota and its value is given as:

\(i = \sqrt{-1}\)

Answer 4

So, in case of iota you can represent \(\sqrt{-4}\) very well as :

\[\sqrt{-4} = \sqrt{-1} \times \sqrt{4} = i(\pm 2) \implies \pm 2i\]