Euler's formulaEuler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x: where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine").
Complex numberIn mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the , and b is called the . The set of complex numbers is denoted by either of the symbols or C.
FirefoxMozilla Firefox, or simply Firefox, is a free and open-source web browser developed by the Mozilla Foundation and its subsidiary, the Mozilla Corporation. It uses the Gecko rendering engine to display web pages, which implements current and anticipated web standards. In November 2017, Firefox began incorporating new technology under the code name "Quantum" to promote parallelism and a more intuitive user interface. Firefox is available for Windows 7 or later versions, macOS, and Linux.
MozillaMozilla (stylized as moz://a) is a free software community founded in 1998 by members of Netscape. The Mozilla community uses, develops, publishes and supports Mozilla products, thereby promoting exclusively free software and open standards, with only minor exceptions. The community is supported institutionally by the non-profit Mozilla Foundation and its tax-paying subsidiary, the Mozilla Corporation.
Mozilla CorporationThe Mozilla Corporation (stylized as moz://a) is a wholly owned subsidiary of the Mozilla Foundation that coordinates and integrates the development of Internet-related applications such as the Firefox web browser, by a global community of open-source developers, some of whom are employed by the corporation itself. The corporation also distributes and promotes these products. Unlike the non-profit Mozilla Foundation, and the Mozilla open source project, founded by the now defunct Netscape Communications Corporation, the Mozilla Corporation is a taxable entity.
Firefox version historyFirefox was created by Dave Hyatt and Blake Ross as an experimental branch of the Mozilla browser, first released as Firefox 1.0 on November 9, 2004. Starting with version 5.0, a rapid release cycle was put into effect, resulting in a new major version release every six weeks. This was gradually accelerated further in late 2019, so that new major releases occur on four-week cycles starting in 2020. Firefox early version history In March 2011, Mozilla presented plans to switch to a faster 16-week development cycle, similar to Google Chrome.
Mozilla ThunderbirdMozilla Thunderbird is a free and open-source cross-platform email client, personal information manager, news client, RSS and chat client that is operated by the Mozilla Foundation's subsidiary MZLA Technologies Corporation. Thunderbird is an independent, community-driven project that is managed and overseen by the Thunderbird Council, which is elected by the Thunderbird Community. The project strategy was originally modeled after that of Mozilla's Firefox web browser and is an interface built on top of that web browser.
Display resolutionThe display resolution or display modes of a digital television, computer monitor or display device is the number of distinct pixels in each dimension that can be displayed. It can be an ambiguous term especially as the displayed resolution is controlled by different factors in cathode ray tube (CRT) displays, flat-panel displays (including liquid-crystal displays) and projection displays using fixed picture-element (pixel) arrays. It is usually quoted as , with the units in pixels: for example, means the width is 1024 pixels and the height is 768 pixels.
Display deviceA display device is an output device for presentation of information in visual or tactile form (the latter used for example in tactile electronic displays for blind people). When the input information that is supplied has an electrical signal the display is called an electronic display. Common applications for electronic visual displays are television sets or computer monitors. Electronic visual display These are the technologies used to create the various displays in use today.
Plasma displayA plasma display panel (PDP) is a type of flat panel display that uses small cells containing plasma; ionized gas that responds to electric fields. Plasma televisions were the first large (over 32 inches diagonal) flat panel displays to be released to the public. Until about 2007, plasma displays were commonly used in large televisions. By 2013, they had lost nearly all market share due to competition from low-cost LCDs and more expensive but high-contrast OLED flat-panel displays.
Mozilla FoundationThe Mozilla Foundation (stylized as moz://a) is an American non-profit organization that exists to support and collectively lead the open source Mozilla project. Founded in July 2003, the organization sets the policies that govern development, operates key infrastructure and controls Mozilla trademarks and copyrights. It owns two taxable subsidiaries: the Mozilla Corporation, which employs many Mozilla developers and coordinates releases of the Mozilla Firefox web browser, and MZLA Technologies Corporation, which employs developers to work on the Mozilla Thunderbird email client and coordinate its releases.
Computer terminalA computer terminal is an electronic or electromechanical hardware device that can be used for entering data into, and transcribing data from, a computer or a computing system. The teletype was an example of an early-day hard-copy terminal and predated the use of a computer screen by decades. Early terminals were inexpensive devices but very slow compared to punched cards or paper tape for input, yet as the technology improved and video displays were introduced, terminals pushed these older forms of interaction from the industry.
Sine and cosineIn mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted simply as and .
Terminal (telecommunication)In the context of telecommunications, a terminal is a device which ends a telecommunications link and is the point at which a signal enters or leaves a network. Examples of terminal equipment include telephones, fax machines, computer terminals, printers and workstations. An end instrument is a piece of equipment connected to the wires at the end of a telecommunications link. In telephony, this is usually a telephone connected to a local loop.
Complex planeIn mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
Argument (complex analysis)In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in Figure 1. It is a multivalued function operating on the nonzero complex numbers. To define a single-valued function, the principal value of the argument (sometimes denoted Arg z) is used. It is often chosen to be the unique value of the argument that lies within the interval .
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Complex conjugateIn 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 and are real numbers then the complex conjugate of is The complex conjugate of is often denoted as or . In polar form, if and are real numbers then the conjugate of is This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: (or in polar coordinates).
Law of cosinesIn trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite respective angles and (see Fig. 1), the law of cosines states: The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then and the law of cosines reduces to The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.
Abraham de MoivreAbraham de Moivre FRS (abʁaam də mwavʁ; 26 May 1667 - 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He moved to England at a young age due to the religious persecution of Huguenots in France which reached a climax in 1685 with the Edict of Fontainebleau. He was a friend of Isaac Newton, Edmond Halley, and James Stirling.
