what is i?

$$\sqrt{-2}=\sqrt{(-1)(2)}=\sqrt{-1}\sqrt{2}=\imath\sqrt{2}.$$

$$\sqrt{-35}=\imath\sqrt{35},$$    etc.

i is stande for a negative square root of a number 

such as 2i=$${\sqrt{-{\mathtt{2}}}}$$ , 35i=$${\sqrt{-{\mathtt{35}}}}$$ 135i=$${\sqrt{-{\mathtt{135}}}}$$e.t.c, coz when you type negative square root of something to the calculator , "error" will be shown , the mathematician design a symbol of negative square root of a number, 

have you learnt these: i=1, i^2=-1,i^3=-1,i^4=1??? 

sorry, I made a mistake on "have you learnt these: i=1, i^2=-1,i^3=-1,i^4=1??? " IT SHOULD BE" i=i, i^2=-1,i^3=-i,i^4=1

i is the base unit of the imaginary number system.

 $$i=\sqrt{-1}$$