phasor, its module and phase angle, inductive and capacitive reactances , " Video 2, 3 ”

Introduction to phasor, inductive and capacitive reactances.
From Euler's formula e^(x) = cos(x) + j.sin(x), where cos(x) represents the real part of e^(x) and j.sin(x) the imaginary part of e^(x), we see that a function such as V(t) = cos(W.t) or I(t) = cos(W.t) represents the real part of e^(x). We therefore express V(t) or I(t) as the real part of e^(x). Then, using the modulus and phase of a complex number, we obtain a function of V(t) or I(t) expressed in modulus and phase. This transforms an expression for V(t) or I(t) that depends on the variable t, into an equivalent expression for V or I in the frequency domain that no longer depends on the variable t .
V(t) or I(t) in the time domain becomes V or I, and these are in modulus and phase form, and V or I is called a voltage phasor or a current phasor.
The term (jwt) represents the frequency [in Hz] or pulsation [in Rad/s] of the phaser. The frequency or pulsation of a voltage or current source is constant, which is why, to simplify phaser writing, we don't mention the term jwt designating its frequency. Whenever we write a phasor, the term (jwt) is always implicitly present. A phasor is therefore a frequency quantity. The reactances XL=j.W.L and Xc=-j/(W.C) result from the quotient of two phasors. However, neither XL nor Xc is a phasor, since they do not reflect the real part of e^(x) = cos(x) + j.sin(x) , but rather derive from the derivatives.
Note: When dealing with a circuit with several voltage and current sources whose pulsations, and therefore operating frequencies, are different, we need to analyze the circuit via each individual source, then superimpose the individual results. The superimposition of results is obviously carried out in the time domain, where there is a single variable t . Superimposing individual results in the frequency domain, where there are several different frequencies, is simply incompatible and inconsistent.