What comes after the square root of negative one? (see link)
I will be very impressed if you know the answer
(PS - the answer is not the square root of negative 2
)
It depends on what part of the number you are advancing. The square root of -1 is i. It has been in use for over four hundred years for solving quadratic equations in algebra that do not have answers in the domain of real numbers. In algebra, the "foil" method is used to prove that the "roots" of an equation reform to become the equation. FOIL stand for first, inner, outer, last because when you multiply 2 single order equations like (x+1)*(x+1), you get (X"squared" + 2X + 1). When you "set" this equation equal to zero, you will find that there is only one answer to it (-1). That is what is called the factor, or root of the equation. The problem arises when going the other direction to find the "factors" or "roots" of the equation. (for example:
(X"squared" + 1) = 0 breaks into (x-i)*(x+i) so that (-i)*(i) = negative 1 (implied by the minus sign) times "the square root of negative one" times "the square root of negative one" which = +1, and the other 2 terms cancel out (+xi - xi). That is the reason for the existence of "i" (the square root of -1).
Now, if you advance the digit inside the square root symbol (-1), you could advance it in one of two directions. you could add 1 (the square root of zero) which would be equal to zero. You could subtract 1, and then indeed your answer would be "the square root of -2" which would further simplify to (the square root of 2)*i (Approx. 1.414*i) if you advance the power of the root, again you could go either direction. -1 to the zero power equals 1. (any number to the zero power equals 1). Then, negative one to the first power equals -1. Then, negative one squared equals 1 again. and so on, "ad infinitum" as they say. If anyone would like to know more about math, or how to interpret silly math questions, please feel free.
Mathematics is nothing more than a way to model the visible/sensory world. In it's simplest form you can count how many apples you have. Complex numbers (powers of "i") are useful for modeling very complex interactions. They are used extensively in electronics, and quantum physics.
Now, for my next post, I will tackle the question at hand. (What lies beyond the end of the universe.)