How can I implement a complex sinusoidal function? The following is the 2d complex sinusoidal function,



$u_0$ and $v_0$ represent Fundamental Frequencies in $X$ and $Y$ directions respectively.

How can I represent $j$ (imaginary number)?

Edit: 

here is my use-case:  ...  ...  I need to implement Gabor Filter using both spatial and frequency domain equations. In the link ...  http://www.cs.utah.edu/~arul/report/node13.html  ..., you can see that there are several equations. (14) is the equation of Gabor Filter in spatial domain. (15) is the equation of Gabor Filter in frequency domain. Hence, my question.
One way to represent a complex-valued function in a bitmap is to use one color channel for the real component and one for the imaginary component. For example, rendering a complex plane wave (your equation) with R = real, G = imaginary looks like this (click for shadertoy):