Originally Posted by

**Alexrey** I'm having some serious trouble with the concept of multifunctions. My lecturer went over them briefly and set a few questions in our tutorial but I'm not exactly sure what he wants us to do. For example, find:

[[i^1/6]]

What exactly does he want us to find? Is this question saying "find the multifuncitons of i^1/6? I spent literally a whole day trying to understand multifunctions by reading my lecture notes, going online and reading T. Needhams, Visual Complex Analysis chapter on the subject but have not really made that much progress on the matter. Am I correct in saying that a multifunction is a "function" that has multiple values for the same value of a complex number assigned to it? If so then I think I understand why log(z) is a multifunction, and I'm beginning to see why fractional powers of z are also multifunctions, but surely then {z}^{n} is also a multifunction? We did a section on finding a complex number's "roots of unity", with {z}^{n} having exactly n roots. But like I said, aren't these roots just multifunctions of z?