Is the Data Set Real or Complex Based on DFT Output?

[zak8000]

Homework Statement

A 8-point data set is transformed with a DFT and the resulting array has values
1,2,3,4,5,6,7,8

was the data set real or complex? why?

Homework Equations

The Attempt at a Solution

kind of confused with this question all i know is the discrete Fourier transform converts a sequence into another. i did i previous question by performing the discrete Fourier transform on a signal which was sampled over a frequency but i don't understand this question.

 

[ideasrule]

Have you learned any properties of the real DFT? One property is that the kth element of the output is the complex conjugate of the (N-k)th element, assuming the elements run from 0 to N-1. It's not an immediately obvious property, but you can easily prove it using the DFT equation.