Inverse dft and dft question

if you define the DFT by:
[tex]
X_k = \sum_{n=0}^{N-1} x_n e^{-i 2 \pi \frac{k}{N} n} = DFT\left(x\right)_k
[/tex]
and it inverse DFT by
[tex]
x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{+i 2 \pi \frac{k}{N} n} = IDFT\left(X\right)_n,
[/tex]
then the way to get [itex]x_n[/itex] from [itex]X_k[/itex] using a DFT would be something like,
[tex]
x_n = \frac{1}{N} \left(\sum_{k=0}^{N-1} X_k^* e^{-i 2 \pi \frac{k}{N} n}\right)^* = \frac{1}{N} \left( DFT \left( X^* \right) \right)_n^*
[/tex].
where the asterix represents conjugation. Does that make sense?

jason