Complex number can be viewed either as an ordered pair of numbers, or as a point in the Euclidean plane, or as a two-dimensional vector. Complex number was an early creation of mathematician from western culture. And through out the history of China, I have not heard about the concept of complex numbers.
In Europe, maybe the first large scale adoption and recognition come from the Eulerian school. Though I knows nothing about the Euler's observation and articles, I still feel that the observation and usage of complex numbers made the calculus and complex analysis more powerful.
So from the historical account of the origin of complex number, it maybe the contribution of well-cultivated person from Europe and it is forming the basic aspect of western mathematical history. By using complex numbers, maybe the world the numbers have been extended and people for the first time can consider the solution of arbitrary polynomial equation, and people can further create more sophisticated concept network based on the complex analysis. It is clear that complex analysis is the starting point of Riemann and he used the knowledge of complex analysis to research manifold, to establish a full set of theoretical tools to analysis the structure and distribution of prime numbers, the probability and Riemannian geometry.
Complex analysis can also be extended to the study of dynamical systems and differential geometry. Anyway, the mathematics behind complex numbers is rich and in large extent form the basic nature of modern mathematics. Today, if a young man want to enter the world of mathematical analysis , complex numbers form a basic basis and it is like a tree, along which we can go to deeper and wider world.
It is said that the basic fabric of the world is made by mathematics. I believe in the world of numbers, complex number as a stand alone world and the greatest one can lead people to appreciate the great power of complex analysis.
Chinese mathematics mainly focus on fulfilling specific tasks about test and examinations. And for the beauty of mathematics, school education concerns less and choose to neglect it. I believe that in order to perceive the great power of mathematics, painting and classical music courses would help Chinese students to appreciate the beauty of nature and the power of mathematical beauty.