Question

why mathematicians called iota "i" an imaginary number?search atleast 5 different cases where real number system gets fail to provide its solution for example x power 2 + 1=0
x power 2 =-1 or x=underroot -1 there is no real number in real number system whose square is negative........please solve this question will get a medal

Answer 1

I know that the first tIme intro to imaginery no. seems to be very befuddeling.

But you have to admit that nature have fabricated this number in itself thread by thread mysteriously...

You can think of i as no. which when multiplied with the coordinates of most of the geometries:

1.)Euclidean Geometry
2.)Non-Euclidean Geometry(In which euclid's fifth postualate is false..such as):

a.)Hyperbolic Geometry
b.)Minkowskian Geometry
etc..ANd the list continues

..ok coming back...you can envision i as a no. which when multiplies rotates a point in space 90 degree by left...

Appllications of I:

1.) First of all ..most important point/application...IT's use to specify rotation in geometry(most important point..al the other applications revolve around this application/point)
2.)IT's used in quantum mechanics heavily(e.g. in Wave function)
3.)It' used in AC circuit analysis
4.)It's also used in computer gfx .(envision a world without i and the battlefield/SMITE/FIFA will be a very low gfx game)
5.)Imagine without the concept of i there will be no euler formula's on which FFT is build and without those FFT/DFT there will be no way for signal sampling(simple playing with signals)....it's equivalent to no WifI,Internet,Mobile,Satellite communications,etc..

LInks to checkout(I hope these will help):

http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/
http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/
http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/
http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/

Answer 2

Rather than "i", It is called the Operator "j" in the electronics world. So it is an important tool that has a practical application. In electronics there exists reactance (both inductive and capacitive) which combines with resistance to form a resultant impedance. Operator "j" is used to designate this reactance. -j for capacitance reactance and j for inductive reactance.

Just to let you know @daniyal.ali that it is not a silly math game, even though imaginary it has a real use.