Complex numberNumber with a real and an imaginary partA complex number z = a + bi can be visually represented as a pair of numbers (a, b) forming a position vector (blue) or a point (red) on an Argand diagram, representing the complex plane.
Phase (waves)Plot of one cycle of a sinusoidal function. The phase for each argument value, relative to the start of the cycle, is shown at the bottom, in degrees from 0° to 360° and in radians from 0 to 2π.In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic functionF{\displaystyle F} of some real variable t{\displaystyle t} (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t{\displaystyle t}.
Absolute valueIn mathematics, the absolute value or modulus of a real numberx{\displaystyle x}, denoted |x|{\displaystyle |x|}, is the (non-negative) magnitudeof x{\displaystyle x}measured without regard to its sign. Namely, |x|=x{\displaystyle |x|=x} if x{\displaystyle x} is a positive number, and |x|=−x{\displaystyle |x|=-x} if x{\displaystyle x} is negative (in which case −x{\displaystyle -x} is positive), and |0|=0{\displaystyle |0|=0}.
E (mathematical constant)Base of natural logarithmsThe number e is a mathematical constant that is the base of the natural logarithm and exponential function. It is approximately equal to 2.718281828459045235360287471352e plays important and recurring roles across mathematics.
Representation theoryBranch of mathematics that studies abstract algebraic structuresRepresentation theory studies how algebraic structures "act" on objects. A simple example is the way a polygon is transformed by its symmetries under reflections and rotations, which are all linear transformations about the center of the polygon.Representation theory is a branch of mathematics that studies abstractalgebraic structures by representing their elements as linear transformations of vector spaces.
Imaginary unitThe imaginary unit, usually denoted by i, is a mathematical constant that is a solution to the quadratic equationx = −1, which is not solved by any real number. Any real-number multiple of the imaginary unit is called an imaginary number.
Exponential functionMathematical function, denoted exp(x) or e^xIn mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted ex{\displaystyle e^{x}} or expx{\displaystyle \exp x}; the latter is preferred when the argument x{\displaystyle x} is a complicated expression.
PhysicsScientific field of studyPhenomena and processes of physics’ various domains, clockwise from the upper left: a Newton's cradle (classical mechanics), entropic changes in a snowflake (thermodynamics), a Chladni figure (waves, oscillations & acoustics), the aurora borealis (geophysics & electromagnetism), an insect floating across a pond (fluid mechanics & biophysics), gravitational lensing (astrophysics, optics & relativity), the double-slit experiment (quantum mechanics), and a Feynman diagram of beta decay (nuclear physics & particle physics).Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.
MultiplicationArithmetical operationFour bags with three marbles per bag gives twelve marbles (4 × 3 = 12).Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result.Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
WaveDynamic disturbance in a medium or fieldSurface waves in water showing water ripplesIn mathematics and physical science, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency.*As an Amazon Associate I earn from qualifying purchases.