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In this work we present several computational results on the complex biharmonic problems. First, we derive FFTRR based fast algorithms for solving Dirichlet and Neumann type complex Poisson problems in the complex plane. These are based on the use of fast Fourier transform (FFT), analysis based recursive relations (RR) in Fourier space, and high order quadrature methods. Our second result is the application of these fast Poisson algorithms to solving four types of inhomogeneous biharmonicdoi:10.1093/imanum/drv033 fatcat:fqpk3sbpgrdmjbzji4bzr4b5by