Fourier coefficients, polar coordinate simplification

by Piol   Last Updated November 09, 2018 00:20 AM

Just wanting to clarify how an exponential representation can be simplified. For example in a question regarding Fourier coefficients the form of the coefficients are $X_{-1} = -2.5e^{-j\pi/6}$ and $X_1 = -2.5e^{j\pi/6}$. But in the solutions they are simplified to $X_{-1} = 2.5e^{5j\pi/6}$ and $X_1 = 2.5e^{-5j\pi/6}$.

So from what i can see, for the $-1$ in front of the exponential, it was recognised as $-1=e^{j\pi}$, so there was an addition of $\pi$ to each. But for $X_1$ shouldn't that mean it becomes $2.5e^{7\pi j/6}$?

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