# Math Help - conjugate representation

1. ## conjugate representation

For $n\in\mathbb{Z}$ and a fixed $t\in\mathbb{T}$, the unit circle in the complex plane,

How can I show that $\overline{t}^n$ can be written as a linear combination of powers (in Z) of t?

2. Originally Posted by moesizlac
For $n\in\mathbb{Z}$ and a fixed $t\in\mathbb{T}$, the unit circle in the complex plane,

How can I show that $\overline{t}^n$ can be written as a linear combination of powers (in Z) of t?
.

$t\in T\Longrightarrow \overline{t}=t^{-1}$ , so...

Tonio

3. Oh of course! I feel silly for asking now :S

Thank you!