pulykamell pretty much nailed it there, but I do have a few things to add:
When using complemetary colors, proportion is the key.
If you were painting on canvas and you wanted shadows in your painting, you would not add black to your basic hue - even a small amount of black would “distort” your color and look very unnatural. If you were to add a small amount of a complement, though, you’d “tone down” your basic hue, making a very natural looking shadow. If you mixed equal amounts of complements, the result would be a muddy, bland, non-color.
The human eye looks for contrast. If there’s contrast, the eye gets “excited” - a monochrome palette is soothing, but can easily get boring. If there’s too much contrast, the eye gets “seasick” for lack of a better word, and your brain compensates for this by mentally blending the colors into that muddy non-color.
Similarly, if we were talking about clothing, you could wear a bright blue shirt and select a tie with a bit of orange in it (and this does NOT have to be a pumpkin orange - you could go with a peachy-orange, a reddish-orange terracotta, a pale yellow-orange). If you were to wear that same bright blue shirt with a pair of bright orange pants, you’d look silly.
I teach color theory to my polymer clay students, but I’m much better at showing then telling, so if the above makes little sense, I can try again 
Here’s a thing, though, I always tell my students about color: yes, it’s important to use color wisely if you’re going to do visual art, but people worry too much about the details sometimes. If you get dressed in the morning and people don’t point at your outfit and snicker, chances are good that you have a basic working knowledge of color theory.
One last thing - if you don’t think complementary colors can work well together, think about Christmas (red & green), Easter (purple & yellow) and football (blue & orange). Again, the proportions of these colors used together create visual excitement, and marketing people use this well!
