mw = 10
dw = 0.7
wx = exp(5)

s0 = Slider[-mw,mw,dw]
u0 = Slider[-mw,mw,dw]
parallelY0 = Curve[log(abs(exp(s0) + i * t)), arg(exp(s0) + i* t), t, -wx, wx]
parallelX0 = Curve[log(abs(t + i * exp(u0))), arg(t + i* exp(u0)), t, -wx, wx]

s1 = Slider[-mw,mw,dw]
u1 = Slider[-mw,mw,dw]
parallelY1 = Curve[log(abs(-exp(s0) + i * t)), arg(-exp(s0) + i* t), t, -wx, wx]
parallelX1 = Curve[log(abs(t - i * exp(u0))), arg(t - i* exp(u0)), t, -wx, wx]




s1 = 0.01
u1 = 0.01
ParallelY1 = Curve[ln(abs(s1 + i* t)), arg(s1 + i* t), t, -500, 500]
parallelX1 = Curve[log(abs(t + i * u1)), arg(t + i* u1), t, -500, 500]