Abstract:  In this paper，the complex function plane is used to replace the real plane of the 
traditional Oxy co- ordinate system，and Euler＇s formula expressed in the form of complex 
exponential is also introduced here to de- scribe and analyze the plane kinematics problem． 
Thus，the confusion and the tedious vector analysis caused by the operation rules of point product 
and cross product in the traditional real plane are avoided． The instantaneous coor- dinate system 
is introduced，and the conclusion is completely consistent with the classical theory．

Key words:  theoretical mechanics, Plane kinematics, complex function plane, Euler formula