The Marksmith AU

The rotation with no direction

You multiply to rotate, without fixing which way.

Multiplying by $e^{i\theta}$ rotates $\theta$ anticlockwise and leaves the modulus unchanged; clockwise needs a negative exponent. If the modulus changes, your factor was $re^{i\theta}$ and the $r$ must be stated.

Next time: State the direction, and whether the modulus changes.

Try it: Work one on a block