Originally Posted by

**imagemania** 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:

$\displaystyle z^{\frac{6}{7}}=e^{\frac{i\pi}{5}}$

$\displaystyle z^{6}=e^{\frac{7i\pi}{5}+2\pi in}$

$\displaystyle z^{6}=e^{\frac{7i\pi}{30}+\frac{2\pi in}{6}}$

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?