Single/ Double sided spectrum plot
For real-valued sequences, the DFT is always conjugate symmetrical, i.e.

$$X[k]=X^*[N-k],\qquad k=0,1,\ldots N-1\tag{1}$$

where $N$ is the DFT length. From $(1)$ with $X[k]=X_R[k]+jX_I[k]$ it follows that the real part of $X[k]$ is symmetrical, and the imaginary part is anti-symmetrical:

$$X_R[k]=X_R[N-k]\\
X_I[k]=-X_I[N-k]$$

Furthermore, with $X[k]=M[k]e^{j\phi[k]}$ we get for magnitude and phase

$$M[k]=M[N-k]\\
\phi[k]=-\phi[N-k]$$

So for real-valued sequences, you get the above symmetries in the real and imaginary parts, and also in the magnitude and phase. So no matter if you represent the DFT in terms of real and imaginary parts, or in terms of magnitude and phase, a one-sided spectrum (i.e. for indices $0,\ldots, \lfloor N/2\rfloor$) is always sufficient, as long as the sequence is real-valued.