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  2. Imaginary number - Wikipedia

    en.wikipedia.org/wiki/Imaginary_number

    An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]

  3. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi, whose real part is zero. As with polynomials, it is common to write a + 0i = a, 0 + bi = bi, and a + (−b)i = a − bi; for example, 3 + (−4)i = 3 − 4i.

  4. Imaginary unit - Wikipedia

    en.wikipedia.org/wiki/Imaginary_unit

    A simple example of the use of i in a complex number is 2 + 3i. Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system , in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra).

  5. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    When s is a complex number—one that looks like a+b𝑖, using the imaginary number 𝑖—finding 𝜁(s) gets tricky. ... For example, x²-6 is a polynomial with integer coefficients, since 1 ...

  6. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.

  7. Complex plane - Wikipedia

    en.wikipedia.org/wiki/Complex_plane

    for example: z = 4 + 5i, where x and y are real numbers, and i is the imaginary unit. In this customary notation the complex number z corresponds to the point ( x , y ) in the Cartesian plane ; the point ( x , y ) can also be represented in polar coordinates with:

  8. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

  9. Complex polygon - Wikipedia

    en.wikipedia.org/wiki/Complex_polygon

    Thus it has two real dimensions and two imaginary dimensions. A complex polygon is a (complex) two-dimensional (i.e. four spatial dimensions) analogue of a real polygon. As such it is an example of the more general complex polytope in any number of complex dimensions.