The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entities in the Euclidean space with translation assumption and graph neural network approaches. However, real vectors inherently neglect the complex relation structures and lack the expressiveness of embeddings; hence, they may guide the embeddings to be falsely generated which results in alignment performance degradation. To overcome these problems, we propose a novel KG alignment framework, ComplexGCN, which learns the embeddings of both entities and relations in complex spaces while capturing both semantic and neighborhood information simultaneously. The proposed model ensures richer expressiveness and more accurate embeddings by successfully capturing various relation structures in complex spaces with high-level computation. The model further incorporates relation label and direction information with a low degree of freedom. To compare our proposal against the state-of-the-art baseline techniques, we conducted extensive experiments on real-world datasets. The empirical results show the efficiency and effectiveness of the proposed method.