Fourier series representation for trigonometric and complex form base

onceinalifetim
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May i know to obtain Fourier series representation for trigonometric and complex form base on magnitude spectrum and phase spectrum??

what i found is that to get trigonometric form is from phase spectrum, but i don't know how.. can anyone help
 
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Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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