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.

• Your second question isn't something anyone else can answer. It's like asking, "I want to plot 'sin(ωx);', what should 'ω' be?" It depends on what you're trying to accomplish. You can set it to 1 to see what it looks like, and then try other values. Or, if you have a specific use-case in mind, explain that, and then maybe we can help you. Sep 17 '16 at 16:28
• @user1118321, Thank you very much for your response. OK. here is my use-case: ... ... I need to implement Gabor Filter using both spatial and frequency domain equations. In the link ... 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.
– user464
Sep 17 '16 at 16:41