Derivative functions in specific with complex module gives the development of induction motor at start position. in describing the torque of induction motor at position 1,2and 3 a vector control with exponential systems in liouvilles principle gives equality of defining stages in elementary calculation carrying start torque with function of z is derived with positive nth root convection which required the exp(z) as given in Euler's method. Conversation of singularities from 2 and 3 stages complex powers with non-zero sections in logarithmic properties of poles and zeros. initiation of logarithmic complex numbers with function accordance in formulating increases poles and zeros version at tst and tmax in induction motor by carrying slip range to running mode. Considering liouvilles vector a mathematical solution is derived with geometrical structures. A wavelet function of trapezoidal, sinusoidal is calculated in running condition along with stand still position of induction motor. Variable frequency of drives in exponentials with algebraic gives 20% of energy saving in semiconductor drives at industry applications .