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In this paper we point out that using Eulers formula ejθ=cosθ+jsinθand formula eAeB=eA+B+2/1｛A,B｝can largely simplify the evaluation of complex and hyper-complex Fourier transform by turning the multiplicationsof quaternion directly into matrices’addition, thus the numerical process is simplified successively.Additionally,we use a special algebraic summation conventionto reduce the complexity of non-commutivity incalculating the quaternion Fourier transform and the discrete quaternion Fourier transform. This technique isexpected to simplify further the corresponding numerical programme.