The University of Queensland School of Information Technology & Electrical Engineering ELEC3002/ELEC7005 Computational Mathematics for EngineersTutorial Complex #2 Q1 The mapping w =α z +β (α, βboth constant complex numbers) maps the point z =1+ j to the point w = j and the point z = −1 to the point w =1+ j. (a) Determine αand β. (b) Find the region in the w-plane corresponding to the upper half plane Im(z) >0 and illustrate with a diagram. (c) Find the region in the w-plane correspond to the disc 2z<and illustrate with a diagram. (d) Find the fixed points of the mapping. Q2 Find a bilinear mapping that maps z = 0 to w = j , z = − j to w =1and z = −1 to w = 0. Hence sketch the mapping by finding the images in the w-plane of the lines Re(z)
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This note was uploaded on 07/07/2009 for the course ELEC 3002 at Queensland.