Rotation in the plane can be concisely described in the complex plane using multiplication of complex numbers with unit modulus such that the
resulting angle is given by .
For example, multiplication by represents a rotation to the right by and by represents rotation to the left by . So starting with and rotating left twice gives , which is the same as rotating right twice,
, and . For multiplication by multiples of , the possible positions are
then concisely represented by , ,
, and .

The rotation symmetry operation for rotation by is denoted "." For periodic arrangements of points ("crystals"),
the crystallography restriction gives
the only allowable rotations as 1, 2, 3, 4, and 6.