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Are you trying to use trig to get around the problem of square roots of negative numbers?Not really, the only way I can have a negative number is if an object moves faster than the speed of light which is impossible. The main reason was to make a wave function.
Yes Ghost, the error in the simple math example is as Bikerman says, though I'm sorry he revealed it as it can cause amusement to those who do not spot the flaw.