# 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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