sentences:  Suppose a circuit has an input voltage described by the equation
  
  where ω equals 2π×100 Hz, i.e., the input signal is a 100 Hz sine wave with an amplitude of 1 volt.If the circuit is such that for this frequency it doubles the signal's amplitude and causes a 90 degrees forward phase shift, then its output signal can be described by
  
  In complex notation, these signals can be described as, for this frequency, "j"·1 V and 2 V, respectively.The complex gain "G" of this circuit is then computed by dividing output by input