The linear mapping w = α z + β , where α and β are complex constants, maps the point z = 2 + j in the z plane to the point w = 10 + 9j in the w plane, and the point z = 3 – 2j to the point w = 15 – 5j. (a) Determine α and β . (b) Find the region in the w plane corresponding to the left half-plane Re(z) ≤ 0 in the z plane. (c) Find the fixed point of the mapping.

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