Question:
Convert the following (finite) complex Fourier series
![](https://static.wixstatic.com/media/20c892_6071df0f1a254ea2aae4b49d8e54d386~mv2.png/v1/fill/w_78,h_4,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_6071df0f1a254ea2aae4b49d8e54d386~mv2.png)
to a (finite) real Fourier series.
Answer:
Use Euler's formula's seen in step (1) and (2), the bridge that connects exponential and trigonometric functions, by way of complex numbers.
![](https://static.wixstatic.com/media/20c892_4d287ecff149420ebb67adcbdb3e000f~mv2.png/v1/fill/w_78,h_37,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_4d287ecff149420ebb67adcbdb3e000f~mv2.png)
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