In a linear algebra course I helped teach last semester, I had the students go through the exercise of writing down the matrix for "multiplication by i," where the complex numbers are thought of as a two-dimensional vector space with {1,i} as a basis. Then I asked them to recognize the matrix (it's a 90-degree rotation of the plane), and then I asked them for an interpretation of that matrix squared (a 180-degree rotation). One thing to draw from this: for the real line, negation doesn't reflect the line, but instead it's a rotation through another dimension of numbers!
When we went on to differential equations, I tried to convince them that e^(ix) is meaningful using your #2: it is a path around the unit circle since it's the solution to z'=iz, and we already agreed multiplication by i is a 90 degree rotation, and circles are what you get when velocity is orthogonal to vector position. It's a bit tougher to convince someone that x is arclength, though, especially when they aren't too comfortable with complex numbers yet.
When we went on to differential equations, I tried to convince them that e^(ix) is meaningful using your #2: it is a path around the unit circle since it's the solution to z'=iz, and we already agreed multiplication by i is a 90 degree rotation, and circles are what you get when velocity is orthogonal to vector position. It's a bit tougher to convince someone that x is arclength, though, especially when they aren't too comfortable with complex numbers yet.