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The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property...

An imaginary number is the product of a real number and the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number...

Mathematically, imaginary time is real time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary unit i. Imaginary time is...

the Roman numeral for 1 i, imaginary unit, for which i2 = −1 I or In, identity matrix of indeterminate size (or of size n) I, unit interval, which contains...

{\displaystyle -\omega ^{2}A+2\zeta i\omega A+A=e^{-i\varphi }=\cos \varphi -i\sin \varphi .} Equating the real and imaginary parts results in two independent...

The symbol i in mathematical equations may refer to; Imaginary unit (i), for which i2 = -1 Imaginary number Complex number i, an index variable in a matrix...

with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 {\displaystyle i^{2}=-1} ; every complex number can...

logarithms, i {\displaystyle i} is the imaginary unit, which by definition satisfies i 2 = − 1 {\displaystyle i^{2}=-1} , and π {\displaystyle \pi } is...

has e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos...

the imaginary error function (erfi) defined as erfi ⁡ z = − i erf ⁡ i z , {\displaystyle \operatorname {erfi} z=-i\operatorname {erf} iz,} where i is the...

part being their mass in the usual sense, and the imaginary part being the decay rate in natural units. However, in quantum field theory, a particle (a...

Three Imaginary Boys is the debut studio album by English rock band the Cure, released on 8 May 1979 by Fiction Records. It was later released in the...

and imaginary (y) parts: z = x + i y {\displaystyle z=x+iy} for example: z = 4 + 5i, where x and y are real numbers, and i is the imaginary unit. In this...

called the unit complex numbers. This is the set of complex numbers z such that | z | = 1. {\displaystyle |z|=1.} When broken into real and imaginary components...

unit imaginary number, while an uppercase "I" serves to denote an identity matrix. I with diacritics: Ị ị Ĭ ĭ Î î Ǐ ǐ Ɨ ɨ Ï ï Ḯ ḯ Í í Ì ì Ȉ ȉ Į į Į́ Į̃...

{i}{2}}d_{-1}-{\frac {1}{4}}d_{-2}+{\frac {i}{8}}d_{-3}\end{aligned}}} If the quater-imaginary representation of the complex unit i has to be...

fields, for example most imaginary quadratic fields, having no real embeddings which also have {1,−1} for the torsion of its unit group. Totally real fields...

Hebrew The negative imaginary unit (−i), a square root of -1 This disambiguation page lists articles associated with the title -i. If an internal link...

Elements Hamilton proves that if there is an i, j and k there also has to be another quantity h which is an imaginary scalar, which he observes should have already...

Log ⁡ z {\displaystyle \operatorname {Log} z} is the logarithm whose imaginary part lies in the interval ( − π , π ] {\displaystyle (-\pi ,\pi ]} . The...