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Don't need to define "i"--it's fundamental. It's primordial. The fact that it's one of the square roots of -1 (and -i is the other) is a theorem.
'''De Moivre’s Theorem''' is a fundamental statement of [[complex analysis]], where ''i'' represents the square root of (-1):
'''De Moivre’s Theorem''' is a fundamental statement of [[complex analysis]]:
:<math>\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,</math>
:<math>\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,</math>