Quote:
Originally Posted by Argus25
Well yes there is [a step change], because across a certain boundary there is no real solution because you can't take the root of a negative number
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Yes you can!
If you define a number j such that j * j = -1, then a whole new area of maths opens up. You end up with complex numbers of the form (a + j * b) because there is no further simplification possible; they act like 2-dimensional vectors, and the best bit is
all the maths you've already learned so far still works with complex numbers! Real numbers are just a subset of the complex numbers, in the same way that the positive integers are a subset of the real numbers.
Just because you can't count out j of something, absolutely doesn't mean it doesn't exist. 10 ** 0.301 exists -- look in your table of antilogs -- even although you can't write a number down a fractional number of times to insert multiplication signs between them.