cmath

cmath is a standard library module in the Python programming language that provides mathematical functions for complex numbers. It is designed as a counterpart to the real-number-focused math module and operates on Python’s built-in complex type. Functions in cmath accept complex inputs and return complex results; when given real numbers, they are promoted to complex form automatically.

The module exposes a broad range of functions, including exponential, logarithmic, square root, trigonometric, and hyperbolic operations, along with their inverse functions. Common examples are exp, log, log10, sqrt, cos, sin, tan, acos, asin, atan, cosh, sinh, tanh, acosh, asinh, and atanh. In addition, cmath provides helpers for complex-number handling such as phase, which returns the argument (angle) of a complex number, and polar and rect, which convert between rectangular and polar representations. The rect function constructs a complex number from polar coordinates, while polar converts a complex number to its polar form.

Behavior differences from the real-number math module include how domain issues are handled. Because cmath operates on complex numbers, many expressions that would raise a domain error with real inputs instead yield complex results. For example, sqrt(-1) yields 1j, and log(-1) yields a purely imaginary result.

In broader programming contexts, the name cmath also appears in other languages with similar roles. In C and C++, libraries named cmath or math provide standard mathematical functions, with C++ often organizing them under namespaces and paired with the complex facilities in the complex header.