Conservapedia - User contributions [en]

Vector quantity

2008-10-04T15:55:40Z

TankutO: addition

A '''vector quantity''' is physical measurement that contains directional information,<ref>Wile, Dr. Jay L. ''Exploring Creation With Physical Science''. Apologia Educational Ministries, Inc. 1999, 2000</ref> as opposed to a [[scalar quantity]].

Force is an example of a vector quantity.

For example, when an airplane is taking off, the air under the wings is exerting a force in an upward direction, gravity is exerting a force in a downward direction, the engine is exerting a force pushing the plane forward, while winds may be exerting forces from side to side.

Temperature is an example of a scalar quantity. The temperature is simply a number of units: normal body temperature is 37° Celsius. You can't speak of an upward temperature, or a northeast temperature; it has no direction. The temperature [[trend]] however does have a direction ([[up]] or [[down]]).

==References==
<references/>

[[Category:Physics]]
[[Category:Mathematics]]

Variable

2008-10-04T15:47:59Z

TankutO: addition

In mathematics, a variable is a value which usually is the subject or part of a [[function]] and must be subject to change while not affecting the structure behind the function in which it acts.

For example, if we have a function: <math>f(x,y)=x^{2}+3y</math>, then <math>x,y</math> are said to be the variables of the function, <math>f</math>.

Further, <math>f(1,2)=(1)^{2}+3(2)=1+6=7</math>. We change the variable and thus alter the value of the function.

Sometimes a function can have also a [[parameter]]. A parameter is similar to a variable, but is not written like a variable and is thus more similar to a [[constant]]. For example, if we a function: <math>f(x,y) = x^2 + ay</math>, then <math>a</math> is said to be a [[parameter]]. It does not change like the [[variables]] x and y, but it can nonetheless take different values. It is important to clearly distinguish the two concepts.

The [[set]] of all variables upon which a function acts is said to be the [[domain]]. The set of all values that a function can take due to its domain is called its [[range]].
[[category:mathematics]]

User:TankutO

2008-10-04T15:16:35Z

TankutO: typo

==Welcome to my user page==

Well what can I say... I will try to add knowledge to my various fields of interest... I will add more to my user page as it comes to my mind. Greetings everyone!

If you want to write to me you can write on the [[talk page]]!!!!

User:TankutO

2008-10-04T15:16:06Z

TankutO: write to me!

==Welcome to my user page==

Well what can I say... I will try to add knowledge to my various fields of interest... I will add more to my user page as it comes to my mind. Greetings everyone!

I fyou want to write to me you can write on the [[talk page]]!!!!

User:TankutO

2008-10-04T15:15:17Z

TankutO: welcome

==Welcome to my user page==

Well what can I say... I will try to add knowledge to my various fields of interest... I will add more to my user page as it comes to my mind. Greetings everyone!

Complex number

2008-10-04T15:11:16Z

TankutO: addition

A '''complex number''' is a [[number]] composed of two parts - a [[Real number|real]] component and an [[Imaginary number|imaginary]] component, of the form <math>a + bi</math>, where ''a'' and ''b'' are real numbers and <math>i^2 = -1</math>.

Whereas the real numbers can be represented as all the possible points on an infinitely extended [[number line]], to represent all the complex numbers requires the use of a two dimensional coordinate system, usually with the real components on the horizontal axis (the ''abscissa'') and the imaginary components on the vertical axis (the ''ordinate''). This representation is known as the Argand diagram.

The complex numbers form an [[algebraic closure|algebraically closed]] [[field (mathematics)|field]] but do not permit a non-trivial ordering that is preserved under operations. They are the algebraic closure of the [[real numbers]].

Many functions used in real analysis can be extended in to complex numbers using [[Taylor series]]. This is the subject of [[complex analysis]].

One should noted that [[complex]] numbers do not [[Reality|really]] exist in [[nature]], for example everything that one can measure in [[Physics]] for example weight, energy, pressure and so on are all [[real]] [[numbers]]. Rather, they are imaginary objects that are used in formal computations. Still, the result of any computation that pertains to the [[real world]], clearly will be a natural number.

===Polar notation===
The complex number <math>a+bi</math> can also be written in the form <math>\rho e^{i\theta}</math>, where
: <math>\rho^2=a^2+b^2</math> is the square of the number's [[Absolute value|magnitude]]
: <math>\theta=\arctan\frac{b}{a}</math> is the phase
If a line is drawn on the [[complex plane]] (also known as an 'Argand diagram' or the 'Argand plane') from the origin to a given complex number, the length of that line will be <math>\rho</math> and the angle it makes to the real (horizontal) axis will be <math>\theta</math>. This leads to a straight-forward geometric interpretation for multiplication by a complex number: multiplying a complex number by <math>e^{i\theta}</math> is equivalent to an anticlockwise rotation through an angle <math>\theta</math> in the complex plane.
===Complex Numbers as Matrices===
The field F on complex numbers is isomorphic to the field F' of 2x2 matrices of the form
:[a -b]
:[b a],
with <math>a+bi</math> mapping as a function f to the above matrix.
We can see that F and F' are isomorphic because:
The function f is clearly 1-to-1 and onto,
<math>f(x+y)=f(x)+f(y)</math>,
and <math>f(x*y)=f(x)*f(y)</math>.

===In popular culture===
In [[Yvgeny Zamyatin]]'s satirical novel ''[[We (novel)|We]]'', the narrator's psychological distress at contemplating the concept of complex numbers becomes a metaphor for the limitations of totalitarian systems of thought.

==See Also==
*[[Arithmetic with complex number]]

[[Category:Mathematics]]
[[category:complex analysis]]