Integration of principal component analysis (PCA) with random matrix theory (RMT) has been successful in analyzing cross correlations between stock price movements in financial markets. RMT is used as a null hypothesis to distinguish between genuine cross correlations and noises. In this paper, we develop a RMT-aided complex PCA method based on the Hilbert transformation of time series. The complex data thus generated carry dynamic information in a form of instantaneous phase; the conventional PCA is entirely dependent on simultaneous correlations in time. Accordingly RMT is generalized to be adaptable to complex PCA. The data set analyzed here is daily returns in Tokyo Stock Exchange (TSE) spanning from 1996 to 2006. Diagonalization of the complex correlation matrix enables us to find that a small number of the eigenvalues certainly deviate from the RMT prediction. The largest eigenvalue represents a market mode in which all of the stock prices move in a collective way. The eigenvectors of the other remaining large eigenvalues clearly show formation of stock groups as characterized by business sectors and also indicates existence of dynamical correlations between some sectors.