**Use of complex Lie symmetries for differential equations**

**Abstract:**

Lie's approach for solving real differential equations can be extended to the study
of complex Lie symmetries and their use in solving complex differential equations.
A complex ordinary differential equation is a combination of two real
partial differential equations with the constraint of the Cauchy-Riemann
equations which constitutes an over determined system. It is shown that the
resulting system possesses those real Lie symmetries that are obtained by
splitting each complex Lie symmetry of a given complex differential equation.
Further use of a complex Lie symmetry reduces the order of a complex
ordinary differential equation which in turn yields the reduction by two real valued functions.