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Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (, ) or the complex number + =, according to Euler's formula with =, both of which have magnitudes of 1.
In Fluorescence lifetime and spectral imaging, phasor can be used to visualize the spectra and decay curves. [1] [2] In this method the Fourier transformation of the spectrum or decay curve is calculated and the resulted complex number is plotted on a 2D plot where the X-axis represents the real component and the Y-axis represents the imaginary ...
For any complex number written in polar form (such as r e iθ), the phase factor is the complex exponential (e iθ), where the variable θ is the phase of a wave or other periodic function. The phase factor is a unit complex number, i.e. a complex number of absolute value 1. It is commonly used in quantum mechanics and optics.
cis is a mathematical notation defined by cis x = cos x + i sin x, [nb 1] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form).
The hue of the colors of the surface plots in the above figure indicate phase. It can be seen that, while for the rotational symmetric aberrations the phase is either 0 or π and thus the transfer function is real valued, for the non-rotational symmetric aberration the transfer function has an imaginary component and the phase varies continuously.
Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . 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 ...
The solutions to the long line transmission equations include incident and reflected portions of the voltage and current: = + + = / + / When the line is terminated with its characteristic impedance, the reflected portions of these equations are reduced to 0 and the solutions to the voltage and current along the transmission line are wholly ...
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
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