Simple angles question - How to get the position to the right of an object relative to their current direction?

I’m working on a top-down 2D game, so my characters are moved on the X and Y axes, and rotated on the Z axis. If my character is rotated to a certain direction on Z, what is the formula to get the position to that character’s right? Really, all I’m looking to get is a single point that is 3 units to the right of the direction that my character is facing, i.e. would be adjacent to his right ear.

I’ve done something like this on one of my projects. I ended up using an empty gameobject that was a child of my player. I could move the empty gameobject relative to my player’s position and then query its position in world space as well.

emptyGameObject.transform.localPosition;  //local space
emptyGameObject.transform.position;  //world space