“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.”
![“That this subject [of imaginary magnitudes] has hitherto been considered…” quote by Carl Friedrich Gauss](https://sms4smile.com/quotes/img-quotes/acb/carl-friedrich-gauss-9412_adapted_that-this-subject-of-imaginary-magnitude_3134596.jpg)
