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The only reason that we like complex numbers is that we don't like real numbers.
Sep 17, 2025
I tell you, with complex numbers you can do anything.
There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.
The shortest path between two truths in the real domain passes through the complex domain.
The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.
Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.
Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.
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