Why did imaginary numbers become accepted despite being useless?

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muser
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Rafael Bombelli first used them and at the time they were thought to be useless. with other discplines (notably physics) finding a use for 'imaginary' numbers, why wasn't it's use curtailed? afterall if I was paid to fill a room with a 1000 people and could only manage 500. would i be within my rights to tell my employer when they ask, that the 500 missing guests, are imaginary. In my mind the whole SUSY theory is tainted by this crude use of mathemathics. are proponents for and against this stance?
 
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muser said:
Rafael Bombelli first used them and at the time they were thought to be useless. with other discplines (notably physics) finding a use for 'imaginary' numbers, why wasn't it's use curtailed? afterall if I was paid to fill a room with a 1000 people and could only manage 500. would i be within my rights to tell my employer when they ask, that the 500 missing guests, are imaginary. In my mind the whole SUSY theory is tainted by this crude use of mathemathics. are proponents for and against this stance?
:rolleyes: Sounds like you need to learn what imaginary numbers are and how they are used. Your example makes no sense. Despite their unfortunate name, imaginary numbers have very real and practical uses in describing the world. The day for campaigning against those crazy "imaginary" numbers is long gone.
 
You would appreciate imaginary numbers if you saw the calculation savings that result from considering a sinusoid to be the projection of the tip of a vector rotating in the real-imaginary plane.

You should enjoy them for many reasons, but this is one notable practical example.