Abstract| We address spherical waves complexi¯ed by a complex shift in a coordinate of the point source. These waves have been studied since the early 1970s in both time-harmonic and non-time-harmonic cases as exact localized solutions of the wave equation. We deal with the fundamental mode described by u = f(µ¤) R¤ , where R¤ = p x2 + y2 + (z ¡ ia)2, a > 0 is a free positive constant, µ¤ = R¤¡ct is a complex phase and f(µ¤) is an arbitrary function describing the waveform. Such a function satis¯es the inhomogeneous wave equation uxx+uyy+uzz¡c¡2utt = F with a certain source function F = F(x; y; z; t), which is a generalized function supported by a 2D surface in the real 3D physical space. Here, c > 0 is the constant wave speed. The function F is dependent on the waveform f as well as on the de¯nition of the branch of the square root in the \complex distance" R¤. Unlike several earlier studies, in which sources in the complex space were discussed, we focus on explicitely ¯nding the source function F in the rea