While the complex form has an imaginary component, after the necessary calculations are performed in the complex plane, its real value can be extracted giving a real valued equation representing an actual plane wave.

In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave.

The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.

There are two maxima of the imaginary component ( the absorptive index ) of water, one at the microwave frequency, and the other at far ultraviolet ( UV ) frequency.

where j is the imaginary unit, V ( ω ) is the voltage component at angular frequency ω, G ( ω ) is the real part of the current, called the conductance, and C ( ω ) determines the imaginary part of the current and is the capacitance.

The symmetric component of the brightness distribution only contributes to the real part of the complex visibility, while the anti-symmetric component only contributes to the imaginary part.

which represents an evanescent wave because the y component is imaginary.

is the wave number, j is the imaginary unit, and ψ ( r ) is the time-independent, complex-valued component of the propagating wave.

In general, impedance has a complex value ; this means that loads generally have a resistance component ( symbol: R ) which forms the real part of Z and a reactance component ( symbol: X ) which forms the imaginary part of Z.

Specifically, the imaginary component ω of the complex frequency s =-σ + iω corresponds to the usual concept of frequency, viz., the speed at which a sinusoid cycles, whereas the real component σ of the complex frequency corresponds to the degree of " damping ".

In absorbing materials, like metals, it is related to the electronic absorption spectrum through the imaginary component of the complex refractive index.

The psychoanalyst Jacques Lacan famously found inspiration in the Borromean rings as a model for his topology of human subjectivity, with each ring representing a fundamental Lacanian component of reality ( the " real ", the " imaginary ", and the " symbolic ").

* Reactance ( electronics ), the imaginary component of AC impedance

The filter has a real and an imaginary component representing orthogonal directions.

To avoid these negative RGB values, and to have one component that describes the perceived brightness, " imaginary " primary colors and corresponding color-matching functions have been formulated.

However, the roots are not necessarily real ; they may include complex numbers with a non-zero imaginary component.

ISO 3166 never assigns country codes beginning with " X ", these codes being assigned for privately customized use only ( reserved, never for official codes )— for instance, the ISO 3166-based NATO country codes ( STANAG 1059, 9th edition ) use " X " codes for imaginary exercise countries ranging from XXB for " Brownland " to XXR for " Redland ", as well as for major commands such as XXE for SHAPE or XXS for SACLANT.

For instance, the polynomial g ( X )= X < sup > 2 </ sup >+ 1 with real coefficients has precisely deg ( g )= 2 roots in the complex plane ; namely the imaginary unit i, and its additive inverse − i, and hence does have distinct roots.

For instance, CNN recently portrayed the Samburu practice of young men giving a large number of beads to a particular girl as tantamount to rape, and erroneously stated that no research exists on the tradition despite the fact that anthropological portrayals based on long term studies show it to be largely akin to the U. S. practice of “ going steady .” In a 2009 article MSNBC took readers on a tour through imaginary places purported to be in Samburu District, while asserting that ethnic conflict between Samburu and the neighboring Pokot was the result of both sides starving because they had more cattle than the rangelands could support, although the reporter did not indicate how having too many cattle could make people starve.

Occasionally, indeed, they were altogether of a quaintly humorous character, introducing, for instance, the alleged wonderful discoveries of an imaginary Professor Monkhouse ".

For instance, it is known that the colloquial use of the term tsar for the All-Russian Emperor in 1721 – 1917 is strictly incorrect, because in this period the term tsar was used in the sense of monarch only for subsidiary ( and partially imaginary ) polities ( with the exception of Poland, at least from 1815 to 1830 ).

From the first equality we can for instance conclude that when the variation of the argument of f ( iy ) is positive, then f ( z ) will have more roots to the left of the imaginary axis than to its right.

David E. Schultz, however, believes Lovecraft never meant to create a canonical Mythos but rather intended his imaginary pantheon to merely serve as a background element.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

The field lines are the paths that a point positive charge would seek to make as it was forced to move within the field ; they are however an imaginary concept with no physical existence, and the field permeates all the intervening space between the lines.

Note, however, that a language wishing to index arrays from 1 could simply adopt the convention that every " array address " is represented by a ′ = a – s ; that is, rather than using the address of the first array element, such a language would use the address of an imaginary element located immediately before the first actual element.

This job did not last long, however, as he was soon dismissed for publishing articles about imaginary animals which he had dreamed up ( though this furnished further material for Švejk ).

In an interview with the Associated Press at the time of the book's release, however, Ventura denied any plans for a presidential bid, stating that the scenario is only imaginary and not indicative of a " secret plan to run ".

He has however consistently tried to modify this view of his concerns: " I prefer to speak of the imaginary, or of consciousness.

Amputees can also carry out imaginary movements of their phantom limbs however these movements do not lead to a feeling that the phantom limb has changed position.

He is however very eager to understand imaginary numbers, which are mentioned in his maths lesson.

The resistance, however, is not enough to characterize the dipole impedance, as there is also an imaginary part —— it is better to measure the impedance.

When dealing with the moral behaviour of adults, however, Samuel Croxall asks, with reference to political alarmism, " when we are alarmed with imaginary dangers in respect of the public, till the cry grows quite stale and threadbare, how can it be expected we should know when to guard ourselves against real ones?

Shakespeare's play As You Like It is set in the Forest of Arden, however it is an imaginary version incorporating elements from the Ardennes forest in Thomas Lodge's prose romance Rosalynde and the real forest ( both as it was then, subjected to deforestation and enclosure, and the romanticized version of his youth ).

The imaginary bubble, however, is misshapen by gravity, causing turns to be much tighter and slower at the top, and wider and faster at the bottom, and is sometimes referred to as a " tactical egg ".

The only fantastic element, however, is the narrator's entry into the afterlife, where he meets with his dead wife and dog, and with the imaginary animals he and his wife invented as traveling companions, as well as a host of other friends.

And if the initial hesitations and the abrupt about-face to the Gaddafi regime may be an element in common with the behaviour of other countries, however, Italy is the only international actor that has long sought to " cling to an imaginary role of mediator ", of which it lacked both the necessary opower and authority.

It does however have some inventive and original ideas, including an autopilot and collision detection device for Martian fliers, and the creation of the Lotharians, a race of ancient martians who have become adept at telepathic projection, able to create imaginary warriors that can kill, and sustain themselves through thought alone.

The nineteenth-century place names of Calcutta, however, appear on this map, thus suggesting we read this imaginary city with the colonial city as a frame of reference.

The story is set in an imaginary American town that has gone bankrupt.

which has a pole in ( zero imaginary part ).

For real values of, we have and for purely imaginary we have hence has a limit at 0 ( i. e., ƒ is complex differentiable at 0 ) if and only if.

Don Quixote has a run-in with traders from Toledo, who " insult " the imaginary Dulcinea, one of whom severely beats Don Quixote and leaves him on the side of the road.

If any part of the ball reaches any part of the imaginary vertical plane transected by this line while in-bounds and in possession of a player whose team is striving toward that end of the field, this is considered a touchdown and scores six points for the team whose player has advanced the ball to, or recovered the ball in, this position.

In American and Canadian football a line of scrimmage is an imaginary transverse line ( across the width of the football field ) beyond which a team cannot cross until the next play has begun.

Rust has said he wanted to create an " imaginary bridge " to the East, and he has claimed that his flight was intended to reduce tension and suspicion between the two Cold War sides.

The show was hosted with members of the Ill Out Crew, various staple partners Paul has worked with throughout his career such as Don Newkirk ( who closes engineer Al Watt's imaginary 3 Feet High and Rising game show and also appears on 3rd Bass's The Gas Face .).

During his early period, Heinlein's writing for younger readers needed to take account of both editorial perceptions of sexuality in his novels, and potential perceptions among the buying public ; as critic William H. Patterson has put it, his dilemma was " to sort out what was really objectionable from what was only excessive over-sensitivity to imaginary librarians ".

Perhaps the most famous is the Higgs boson of the Standard Model of particle physics, which — in its uncondensed phase — has an imaginary mass.

First published in the 1960s, her work has often depicted futuristic or imaginary worlds alternative to our own in politics, natural environment, gender, religion, sexuality and ethnography.

The imaginary term j has also canceled out, making Z < sub > 0 </ sub > a real expression, and so is purely resistive.

In fiber optics, a graded-index or gradient-index fiber is an optical fiber whose core has a refractive index that decreases with increasing radial distance from the fiber axis ( the imaginary central axis running down the length of the fiber ).

Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.

Being an equality of complex numbers, one necessarily has equality both of the real parts and of the imaginary parts of both members of the equation.

Volume II has an extensive appendix, most of which is filled with an imaginary travelers ' account of the alternate universe the League is set in, called The New Traveler's Almanac.

It is has even been suggested by one modern scholar that imaginary characters and situations might have been a feature of the poetic tradition within which Archilochus composed, known by the ancients as iambus.

If such a Hamiltonian has a unique lowest energy state with a positive real wave-function, as it often does for physical reasons, it is connected to a stochastic system in imaginary time.

The imaginary play The King in Yellow has two acts and at least three characters: Cassilda, Camilla, and the King in Yellow.

While there has to be some elements of real life history to the setting under most definitions, the " detective " may be a real-life historical figure, e. g. Socrates, Jane Austen, Mozart, or a wholly imaginary character.