Phasor, addition and multiplication of complex numbers and phasors , " EXO 2 - Vidéo 2, 2 "

To transform a sinusoidal current or voltage in the time domain which depends on the variable t, into a current phasor or voltage phasor in the frequency domain which does not depend on the variable t , in order to be able to analyse a circuit in the frequency domain without taking time t into account.
A phasor is a complex number expressed in terms of modulus and phase where the variable t no longer exists. A phasor depends on frequency, and since frequency (or pulsation in [Rad/s]) is always constant, it is not mentioned, although it is implicitly present. In other words, when we perform calculations using phasors, i.e. modulus and phase, we need to remember that we are reasoning in the frequency domain. In other words, PHASOR = frequency domain.
Note: A simple formula is used to transform a SINUS function into COSINUS.
COS(x)=SIN(x+90°). We convert a time-domain current or voltage, presented in SINUS form, into COSINUS and then transform the time-domain COSINUS expression into a frequency-domain phasor.