I wouldn't say it's "just" a convention. That implies it's arbitrary. It might look arbitrary, but it's not: for example, d/dx ((cos x + i sin x)/e^ix) = 0, as

I wouldn't say it's "just" a convention. That implies it's arbitrary. It might look arbitrary, but it's not: for example, d/dx ((cos x + i sin x)/e^ix) = 0, as required. This doesn't hold if you pick (say) e^ix = cos x - i sin x.