In thiswork, a numerical method based on a complex operationalmatrix is utilized to solve high order linear complex differential equations under mixed initial conditions. For this aim, we introduce orthonormal Bernstein polynomials (OBPs), and we obtain their complex operationalmatrix of differentiation. Themain advantage of the proposed method is that by using thismethod complex differential equations reduce to a linear system of algebraic equations which can be solved by using an appropriate iterative method. To, some results concerning the error analysis associated with the present method are discussed. Finally, we give some numerical examples to reveal accuracy and efficiency of the proposed method. Also, the numerical results obtained by this method are compared with numerical results achieved from other existing methods.
