SOLUTION: solve the equation z/z+1 = cos pi/4

Starting equation is

     = .    (1)


Notice that  = ,  so your equation is

     = .


For brevity, I will use t for  , so my equation is

     = t.    (2)


From (2)

    z = t*(z+1)

    z = tz + t

    z - tz = t

    z(1-t) = t

    z =  =  =  = 2.414214  (rounded)


CHECK.   = 0.707107 = .   ! correct !