Facial expression recognition (FER) is a key component in various AI-based systems and has been extensively studied. However, most FER research has focused on clear and simple basic emotions such as happiness and sadness, which are not suitable for real-world applications where numerous many ambiguous and complex emotions exist. Complex emotions are challenging to define and require ample data for each emotion to train a FER model. Moreover, due to their ambiguous nature, these emotions are difficult to annotate. Consequently, the difficulty in constructing comprehensive databases is a significant bottleneck in recognizing complex emotions. In this study, we propose complex emotion recognition method using only a database of basic emotions based through angle-base metric learning. This approach can mitigate the reduction in recognition accuracy caused by insufficient data and allows for the definition of new emotions in the future, unlike general FER tasks that require pre-definition of emotions.