How to Plot modulo function Mod on a function of two variables? [closed]

I know that Plot[Mod[x, 2], {x, -6, 6}] is a Mathematica command to plot the remainder of x over 2 when I range x over reals -6 to 6. How do I plot the same Mod function on a real valued two variable function f(x,y) in the following manner?

Plot[Mod[f(x,y), 2], {x, -6, 6}, {y, -6, 6}]

More details, if needed: This is my exact function f(t,c) = (t/2)*Log[c^2 + 1] + (k/2 - 0.1) Arg[1/(c - I)] where I am varying k as a parameter as shown below.

Manipulate[ Plot[Mod[(t/2)*Log[c^2 + 1] + (k/2 - 0.1) Arg[1/(c - I)], 2 Pi], {t, 2 Pi, 4 Pi}, {c, -100, -4}, PlotRange -> {0, 10}, ClippingStyle -> None], {k, 12, 300}]

Above here is the actual code that I am using.
Thank you

closed as off-topic by Michael E2, m_goldberg, Öskå, MarcoB, Henrik SchumacherAug 5 at 15:06

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