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  2. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number.

  3. 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.

  4. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    This is true for all values of , so the solution set is all real numbers. But clearly not all real numbers are solutions to the original equation. The problem is that multiplication by zero is not invertible: if we multiply by any nonzero value, we can reverse the step by dividing by the same value, but division by zero is not defined, so ...

  5. Numerical analysis - Wikipedia

    en.wikipedia.org/wiki/Numerical_analysis

    It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.

  6. List of unsolved problems in computer science - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    The problem to determine all positive integers such that the concatenation of and in base uses at most distinct characters for and fixed [citation needed] and many other problems in the coding theory are also the unsolved problems in mathematics.

  7. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    All quadratic equations have exactly two solutions in complex numbers (but they may be equal to each other), a category that includes real numbers, imaginary numbers, and sums of real and imaginary numbers. Complex numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation

  8. Complex analysis - Wikipedia

    en.wikipedia.org/wiki/Complex_analysis

    A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a (not necessarily proper) subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are generally assumed to have a domain that contains a nonempty open subset of the complex plane.

  9. Complexity class - Wikipedia

    en.wikipedia.org/wiki/Complexity_class

    A counting problem asks not only whether a solution exists (as with a decision problem), but asks how many solutions exist. [18] For example, the decision problem asks whether a particular graph has a simple cycle (the answer is a simple yes/no); the corresponding counting problem # (pronounced "sharp cycle") asks how many simple cycles has. [19]