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  2. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.

  3. 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.

  4. List of undecidable problems - Wikipedia

    en.wikipedia.org/wiki/List_of_undecidable_problems

    "The problem of deciding whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic", a consequence of the MRDP theorem resolving Hilbert's tenth problem. [5] Determining the domain of a solution to an ordinary differential equation of the form

  5. Complex-base system - Wikipedia

    en.wikipedia.org/wiki/Complex-base_system

    In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary (proposed by Donald Knuth in 1955 [1] [2]) or complex number (proposed by S. Khmelnik in 1964 [3] and Walter F. Penney in 1965 [4] [5] [6]).

  6. List of unsolved problems in mathematics - Wikipedia

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

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  7. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number ...

  8. 5 - Wikipedia

    en.wikipedia.org/wiki/5

    5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5). [1] 5 is the first safe prime, [2] and the first good prime.

  9. Quater-imaginary base - Wikipedia

    en.wikipedia.org/wiki/Quater-imaginary_base

    Most numbers have a unique quater-imaginary representation, but just as 1 has the two representations 1 = 0. 9 in decimal notation, so, because of 0. 0001 2i = ⁠ 1 / 15 ⁠, the number1 / 5 ⁠ has the two quater-imaginary representations 0. 0003 2i = 3· ⁠ 1 / 15 ⁠ = ⁠ 1 / 5 ⁠ = 1 + 3· ⁠ –4 / 15 ⁠ = 1. 0300 2i.

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