Hi,

Roots of unity is a very easy topic for me, though i am misunderstanding one small part of it which i wish to rectify.

Here's an example:

Where n is an integer, i is the complex number and e an exponential.

Now i undertand the use of 2pi i n, as its roots of unity and therefore will go back to being equal to 1.

However i don't understand why we pluck in the 2 pi i n in the second step, rather than the first or the last. By raising to the power that induces the 2 pi i n to appear? Why?

Hope you can help me :)