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The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers , using addition and multiplication .
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]
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.
7: 6 [6] Clay Mathematics Institute: 2000 Simon problems: 15 < 12 [7] [8] Barry Simon: 2000 Unsolved Problems on Mathematics for the 21st Century [9] 22 – Jair Minoro Abe, Shotaro Tanaka: 2001 DARPA's math challenges [10] [11] 23 – DARPA: 2007 Erdős's problems [12] > 934: 617: Paul Erdős: Over six decades of Erdős' career, from the 1930s ...
Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Perelman's solution completed Richard Hamilton's program for the solution of the geometrization conjecture, which he had developed over the course of the preceding twenty years. Hamilton and Perelman's work revolved around Hamilton's Ricci flow , which is a complicated system of partial differential equations defined in the field of Riemannian ...
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. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
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