I don't know who "discovered" complex derivatives, but their applications in different disciplines has been popular for a while. I find it strange that any of these is attributed to some 56-year-old sapling.
"Numerical algorithms based on the theory of complex variable", Lyness, 1967 (paywall)
"Numerical Differentiation of Analytic Functions", Lyness & Moler, 1967 (PDF)
Are you pulling my leg? The sensitivity analysis in various fields requires an accurate estimation of derivatives, and hence they use complex step method instead of finite differencing, e.g. "The Complex-Step Derivative Approximation", Martins, et al., 2003 (example of an application and a simple estimation of the error)