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2. Millennium Prize Problems - Wikipedia

   en.wikipedia.org/wiki/Millennium_Prize_Problems

   The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...

3. Complex number - Wikipedia

   en.wikipedia.org/wiki/Complex_number

   In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation =; every complex number can be expressed in the form +, where a and b are real numbers.

4. List of complex analysis topics - Wikipedia

   en.wikipedia.org/wiki/List_of_complex_analysis...

   Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers.It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.

5. Cauchy–Riemann equations - Wikipedia

   en.wikipedia.org/wiki/Cauchy–Riemann_equations

   In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable.

6. Complex analysis - Wikipedia

   en.wikipedia.org/wiki/Complex_analysis

   Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

7. Argument (complex analysis) - Wikipedia

   en.wikipedia.org/wiki/Argument_(complex_analysis)

   Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...