> quirky work around for negative square roots. I would say that is more of a side effect. I agree it's not a perfect motivation, for teaching purposes. When y

> quirky work around for negative square roots. I would say that is more of a side effect. I agree it's not a perfect motivation, for teaching purposes. When you introduce an answer to the square root of a negative number, questions of soundness might arise. Obviously it's sound, but is that a distraction at the level where complex numbers are introduced? Besides, many people like geometric interpretations: they might feel more 'real' or relevant than an algebraic motivation. /Nonetheless/, I can't agree well defined square roots is just a side effect. The complex numbers are (up to isomorphism) the one and only algebraic closure of the reals. That's a very natural and and useful way look at them for, say, university level maths.