The complex logarithm is a mathematical term that refers to the multivalued function which maps complex numbers to other complex numbers. It is commonly used to calculate the power of numbers in the complex plane. Some synonyms for the complex logarithm include the complex natural logarithm, the logarithmic function, the hyperbolic logarithm, and the transcendental function. Additionally, it is often referred to as the inverse of the exponential function, as it solves equations in which the exponential function is the base. The complex logarithm is an important concept in calculus and other branches of mathematics, and is foundational to many advanced mathematical principles.