why shouldn’t they exist?
they exist as much as begative numbers or square roots exist.
Mathmatically they exist as solutions to equations. You could equally say numbers *are* the defining equation, and map all rules of numbers towards thosenof the corresponding equations.
negative numbers are solutions to sime equations like x+5=2.
rational numbers are solutions to equations like 5*x = 3.
irrational numbers are solutions to x^2 + 7 = 10.
complex numbers are also solutions to similar equations like x^2 + 5 = 1.
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