Imaginary unit

Then, multiplying the second equation of this set by an imaginary unit i and adding the first equation we arrive at one equation with respect to the complex variable < ... 

The imaginary unit i contained in the operator p is essential for the hermitian character of that operator. The operator L>x = A/Ax is not hermitian because... 

Here j is the imaginary unit, co is the angular frequency, and C is the capacitance. For solid electrodes, however, the impedance response deviates from a purely capacitive one and the empirical equation should be used... 

With this notation, the electric charge qo of a monopole equals Qoo-Cartesian dipole components px, py, pz, are related to the spherical tensor components as Ql0 = pz, Qi i = +(px ipy)/y/2, with i designating the imaginary unit. Similar relationships between Cartesian and spherical tensor components can be specified for the higher multipole moments (Gray and Gubbins 1984). 

We consider the trace at t = 0, Tr[Fe /2kBT9 P)e l2kBT] = Tr[PA], which defines the operator A. It is noted that both the flux operator F and the A operator are Hermitian operators, which implies that Tr[Tk4] = Tr[(PA)t] = Tr pt] = Tr[AP] = Tr[PA], that is, the trace must always be real valued. Furthermore, if the trace is evaluated in a basis of real-valued functions, then the trace must be equal to zero, since the operators contain the momentum operator, which also contains the imaginary unit i = T. Using this result, Eq. (5.108) can be written in the form... 

Z, is the real part of the complex number which represents the impedance i = V-L is the imaginary unit Z is the imaginary part... 

Note that in this chapter we use j instead of i for the imaginary unit of the complex in order to distinguish j from the current density... 

---