Ideally, yellow, orange, and green are the most obvious complementary colors for purple, whilst red is not.
However, fashion does not always follow the obvious path and we have seen time and time again designers can pulling it off (or anyone without fear of trying a risky “mix”). Do not forget that clothes are only part of the equation, skin tone, accessories and personal style can play a big role as well. What would be the verdict then? If you feel confident, go for it, otherwise, try to avoid this combination.
One frequently used theory is called “color theory”. It states that you can decide which colors complement each other using a color wheel. The ones directly opposite of each other are seen as complementary.