Discrete Fourier transform of complex time series I am working through previous exam questions for a class I'm currently taking in signal theory, and one problem, although it looks easy, stumps me.  

PROBLEM

Two real $N$-periodic time seires $f_n$ and $g_n$ are given, where $n = 0, 1, 2, ..., N-1$.

In addition, the complex time series $h_n$ is given as

$$h_n = f_n + i g_n$$

and the discrete Fourier transform

$$H_m = F_m + i G_m$$,

where $m = 0,1,. . ., N-1$.

Find the discrete Fourier transofrm $F_m$ and $G_m$ to the time series $f_n$ and $g_n$ expressed through $H_m$

ATTEMPTED SOLUTION

As I said, I'm really stumped here.  Other than writing:

$$F_m = H_m - i G_m$$

and

$$G_m = i (F_m - H_m)$$

I don't see what else to do.  Is this all there is to it?  It seems way too easy, so I'm pretty sure I'm not doing this correctly.

If anyone can give me any help, I would greatly appreciate it!
Proposed answer to my own question:

We have that:

$$F_m = \frac{1}{2}(H_m + H^*_m)$$

and

$$G_m = \frac{1}{2i}(H_m - H^*_m)$$

where $H^*_m$ represents the complex conjugate of $H_m$.