Do I need to be taking supplements while dieting?

Get individual input. The general answer is yes. But i will refer this to nutrition specialists for you. Thanks for asking.
Yes. With reduced calorie intake ("dieting") - some basic nutrients might not be included. So, i always recommend a good , reputable - organic if possible general multivitamin - from as natural sources as possible - along with omega-3s daily. Fiber is always helpful - as well... Good luck!