sqrt

A.F.Beardon Complex Analysis page 13:

```maxima
(%i1) z: sqrt( 1/2*( sqrt(u^2+v^2) + u) ) + %i*(v/sqrt( 2*( sqrt(u^2+v^2) + u) ) );
                      2    2
           sqrt(sqrt(v  + u ) + u)                %i v
(%o1)      ----------------------- + -------------------------------
                   sqrt(2)                              2    2
                                     sqrt(2) sqrt(sqrt(v  + u ) + u)
(%i2) z^2;
                     2    2
          sqrt(sqrt(v  + u ) + u)                %i v               2
(%o2)    (----------------------- + -------------------------------)
                  sqrt(2)                              2    2
                                    sqrt(2) sqrt(sqrt(v  + u ) + u)
(%i3) expand(%);
                          2                    2    2
                         v               sqrt(v  + u )          u
(%o3)        (- ---------------------) + ------------- + %i v + -
                        2    2                 2                2
                2 sqrt(v  + u ) + 2 u
(%i4) radcan(%);
(%o4)                              %i v + u

```