tutorial%20complex%202

# tutorial%20complex%202 - The University of Queensland...

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The University of Queensland School of Information Technology & Electrical Engineering ELEC3002/ELEC7005 Computational Mathematics for Engineers Tutorial Complex #2 Q1 The mapping w = α z + β ( α , β both 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 α and 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 2 z < 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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