Explain Shift property of DFT
But if we see this new vector we can see that here no translation of the signal is done.


You have modified the data in the frequency domain, by multiplying by exp(−j2πkD/N). The translation thus occurs in the time domain. It would be indeed weird if multiplyig a vector by exp(−j2πkD/N) would shift this same vector!

The inverse DFT of [11,3-2j,-1,3+2j] is: [4, 4, 1, 2].

The inverse DFT of [11,-3+2j,-1,-3-2j] is: [1, 2, 4, 4].

The shift property is observed - the signal has been shifted by 2 (modulo 4).