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I am having a hard time understanding why my textbook takes the squared magnitude of the calculated DFT coefficients.

I know in DFT, you would normally take the magnitude to get the spectrum, how come it is the squared magnitude which gives me the spectrum when iam using goertzel?

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When taking a DFT you would also normally use the squared magnitude, which gives the amount of power in a particular frequency bin. Of course you can use whichever you find more informative, but what usually gets quoted or plotted is the power spectrum, which is |DFT|^2.

There's nothing different about the Goertzel algorithm here; if the frequency you feed it is one of the finite set processed by a DFT, Goertzel and an ordinary DFT will do the exact same computation and give the exact same answer (aside from issues like roundoff and error accumulation, which are important but not really the point here).

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