Find the exponential form of the complex number
[e^{\pi i/4} + e^{5 \pi i/12} + e^{7 \pi i/12} + e^{3\pi i/4} + e^{11\pi i/12}
eπi/4+e5πi/12+e7πi/12+e3πi/4+e11πi/12
with proof.
I've graphed each of the points on the complex plane to find that they are separated by an angle measure of pi/6. 2 pairs of 2 points have the same x-coordinate, but negative, but I don't know where to go from there. I know I'm supposed to use the magnitude of the sum of some of the points as well as the symmetry of the diagram, but I'm not sure how.
Thanks!
I have no idea what the answer is but for convenience's sake:
THE QUESTION:
Find the exponential form of the complex number
[eπi/4+e5πi/12+e7πi/12+e3πi/4+e11πi/12
with proof.