Differentiating equation (1.18) with respect to time gives

                                                                                                                              (1.21)

and

                                                                                                              (1.22)

From equation (1.19), we can write

                                                                                                                              (1.23)

where is the complex conjugate of z as shown Figure 1.4. We can also write

                                                                                             (1.24)