The complex structure of a point
in the Plane is defined by the linear Map

and corresponds to a clockwise rotation by . This map satisfies

where is the Identity Map.

More generally, if is a 2-D Vector Space, a linear map such that is called a complex structure on . If , this collapses to the previous definition.

**References**

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*Boca Raton, FL: CRC Press,
pp. 3 and 229, 1993.

© 1996-9

1999-05-26