Abstract: This paper discussed the problems of conjugate operation such as the limit of complex function and complex number，the continuity of a function，the derivative of a function，the integration of complex function，the series etc，and illustrated application of the operation in the series.With new methods in this paper，it especially proved the famous Poisson integral formula which has important applica? tions in function theory and partial differential equations.

Key words: complex, conjugate operation, Cauchy formula, Poisson integral formula