So I'm doing this course about image processing, which algorithm heavy course. Now there's a thing called Fourier transform.

Here's few formulas that is used to explain the basics:

$$C=R+jI$$ $$C^*=R-jI$$ $$C=|C|(\cos(\Theta)+j \sin(\Theta))$$

However, I don't have the slightest of ideas what they mean, what are these variables coming from and what's that round symbol with a dash inside it.

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Here $C$ seems to denote a complex number. $j = \sqrt{-1}$ and $R,I \in \mathbb R$ are the real and the imaginary part of your complex number $C$.
The round thing with a dash in it is the Greek letter theta: $\Theta$.
If $z = |C| e^{j\Theta}$ is a complex number then $\Theta = \arg z$ and $|C|$ is the radius if you think of $\mathbb C$ as $\mathbb R^2$.