See also ComplexNumbersAreYourFriends, but let's not merge them. Both titles are potentially grammatically correct; the one refers to "complex numbers" as a single collective, the other refers to each and every member of that collective.

''Just to be anal retentinve - not quite.  Perhaps, ComplexNumberingIsYourFriend?  "Complex numbers are your friend" is exactly as grammatically correct as "Complex numbers is your friend".''
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A lot of integrals are actually easier to perform using ComplexVariables.  I recommend that everyone study ComplexVariables sometime--especially those who have to write StatisticalSoftware or are involved in MathematicalComputing.  Besides, there needs to be a way to define the SquareRootOfNegativeOne.

''Presumably everyone gets complex numbers in high school, but ComplexAnalysis is another matter, and that's where it gets interesting.''

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ComplexNumbers simply simplify so many things, since they allow you to see the whole picture. From a SignalProcessing perspective, it all has to do with HarmonicOscillation not having a solution of order 1 over the RealNumberField.

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See also ComplexNumbers, FortranLanguage, PythonLanguage
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CategoryMath