Instead of solving Rayleighs equation, Hsiao-Lan Kuo came up with a necessary stability condition which had to be met in order for the fluid to be able to get unstable. To get to this criterion, Rayleighs equation was rewritten and the boundary conditions of the flow field are used.
The first step is to divide Rayleigh's equation by  and multiplying the equation by the complex conjugate of .
In the last step,  is multiplied with its complex conjugate leading to the following equality is used: . For the solution of Rayleigh's equation to exist, both the real and imaginary part of the equation above need to be equal to zero.