The complex numbers allow us to consider scalings and rotations as two instances of the same thing; and by ensuring that negative reals have square roots, we get something where every (non-constant) polynomial equation can be solved: C is the algebraic closure of R.

Quora and StackExchange are fast turning out to be my personalized wikipedia. Unlike the sterilized quality of answers in wikipedia, the learned folks on Quora and SE reaching into their experience and sharing their personable answers, it is (they are) fast becoming my personal treasure trove of knowledge.