The aim of this objective is to compare complex complex valued functions(with one complex variable) with their real valued (with one or two real variables) functions.
– Check with some fundamental functions such as complex exponential functions.
– Look into the the real valued with two-real variables functions encountered in the studying complex functions.
– Look into graphing a real and complex function.
– Compare linear (real and complex) functions, linear approximation of a real and of a complex function and their meanings (use CAS to compare the images of some explicitlydefinedsetsunderthecomplexfunctionandunderitslinearapproximation).
– Check withmulti-valuedfunctions, lookalso into theirgraphs (for examplecomplex power function, complex logarithm function, complex exponential function)
– Check also if all the properties of real powers work also for complex powers.
– Check with trigonometric functions.
– Check with the inversion function, see that it can map lines to circles and it can be reversed.
– Check from the limit of a function perspective.
– Check from the continuous function perspective(for example in the real case we say there should not be any jumps, do we have the same observation in the complex case?).
Write a report on Obj. #2, about 8−9 pages with proper citations, and on a separate page(s) the references (only the ones used in the report), in an MS Word file.
I put report on Obj. #1. You may wanna look at it since report on Obj. #2 is going to be the next report.
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