The plug-and-play (PnP) framework is a powerful recent advancement for solving linear inverse problems in imaging: a strong regulariser can be learned from a denoising task and then reliably applied to solve highly ill-posed problems such as accelerated non-Cartesian MRI reconstruction. When applying PnP to complex-valued MRI data, the common design choice is to denoise the real and imaginary components independently, using an off-the-shelf real-valued denoiser. However, in many diagnostic imaging tasks the phase of the reconstructed image carries clinically relevant information, and this real/imaginary convention offers no explicit guarantee that phase is preserved or correctly regularised. Recent theory further shows that any convex, amplitude-equivariant regularisation functional must be phase-invariant by construction — a property naturally satisfied by regularisers built from the magnitude of complex-linear filter responses, but not, in general, by one applied independently to real and imaginary channels. This project aims to examine these results in the context of learned regularisation functions (e.g. WCRR, MFoE), and empirically studies the real/imaginary versus magnitude-based design choice within PnP reconstruction techniques for accelerated MRI.