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## Main Question or Discussion Point

actually have two questions:

here we have a fourier series..

$$f(t) = \sum c_k e^{2\pi ikt}$$ (c is complex)

if we're trying to express a real function via fourier series, and we do it the following way..

Impose condition: $$\overline{c_k} = c_{-k}$$

$$f(t) = \sum\limits_{k= -n}^n c_k e^{2\pi ikt}$$

then, although the constants would become real, wouldn't the exponents go to zero? why not?

could someone give me more of an intuitive understanding for the "orthogonality" of sine functions? i know the integral definition, but how exactly does this integral dictate what can & can't be expressed in terms of what (ie could you relate the integral definition to the classical sense of the word 'orthogonal')

here we have a fourier series..

$$f(t) = \sum c_k e^{2\pi ikt}$$ (c is complex)

if we're trying to express a real function via fourier series, and we do it the following way..

Impose condition: $$\overline{c_k} = c_{-k}$$

$$f(t) = \sum\limits_{k= -n}^n c_k e^{2\pi ikt}$$

then, although the constants would become real, wouldn't the exponents go to zero? why not?

could someone give me more of an intuitive understanding for the "orthogonality" of sine functions? i know the integral definition, but how exactly does this integral dictate what can & can't be expressed in terms of what (ie could you relate the integral definition to the classical sense of the word 'orthogonal')

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