Please can someone explain to me the exact practical usage of 'The square root of minus one" - it drives me bat-s*#t trying to understand why we even have it.... : (
by 
originallyjustme
ANSWERS: 5
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http://www.fortunecity.com/meltingpot/melwood/368/rootm1d.html http://www.omatrix.com/manual/mlmode_ij.htm Sorry, that is all I can do. Hope that helps!
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They are used frequently in quantum mechanics, particularly in the wave functions of particles.
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Well, at least it gives a way to solve quadratic functions that do not cross the x-intercept. Additionally, later in mathematics it is used to quantify areas and magnitude by setting the imaginary number on its own axis in order to calculate certain vectors. If you never get into this high math, thank your lucky stars and just understand that it is a placeholder used so that can mathematicians can solve other things that make your life easier. If, on the other hand, you plan on becoming an engineer, then use it, understand how to use it, and one day it will make sense. "But father, when will I know that I know everything?" "Trust me, my son. You. Will. Know."
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We use it in electrical systems to describe LCR circuits (Inductance, Capacitance, Resistance) where we have 'imaginary' resistances (called impedances) which means we can work out properties like the resistance of the circuit, how current and voltage operate around the circuit (sometimes voltage lags sometimes it leads, sometimes they are perfectly in phase). It also allows us to have a 'wave function' description for things on a quantum level, where the wave function mulitplied by the complex conjugate of the wave function results in the probability of finding the particle at a location. 'i' is a very useful concept, and its a demonstration on the limitation of human mathematics to describe the universe.
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I think there is a statistical use for that in finding deviations of some such rot; but my old stats book is now holding up my tv, along with my algebra book, so I can't look it up to give you a real answer.( oh, wait, I think i get the wrong-o award. The square root of neg one is like the square root of two; In theory there has to be one, but in practice there is not. 1*1=1 (-1)*(-1)=1 therefore we can not have a square root for -1 This link offers someone else's view on the topic. http://www.rpi.edu/~newbel/misc-publications/mgod.html
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