Complex geometry is a branch of mathematics that studies geometric structures using the principles of complex numbers. It combines ideas from both algebra and geometry, focusing on shapes and spaces that can be described with complex coordinates. This field is essential for understanding various mathematical concepts, including Riemann surfaces and complex manifolds. In complex geometry, researchers explore properties like curvature and topology, which help describe how shapes behave in higher dimensions. The study has applications in several areas, including string theory in physics and algebraic geometry, which examines solutions to polynomial equations.