That's why you first develop a very good intuition of what complex numbers really are, understand Euler's formula (and probably asked to come up with a proof fo

That's why you first develop a very good intuition of what complex numbers really are, understand Euler's formula (and probably asked to come up with a proof for it), and only then move forward. In mathematics, it's really easy and dangerous to think that you understand a concept only because you can memorize it's definitions and properties; any math education should fight this pseudo-understanding and make sure that you really grok it.