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# Long description

This figure consists of two copies of the complex plane side by side, both focused on the upper-right quadrant. The axes are not labelled. On the left-hand diagram a point in the upper-right quadrant is marked with a solid black dot and labelled alpha. A small circular disc is drawn with alpha as its centre and a solid black circle as its boundary. Inside the disc a second point, a little to the right and below the point alpha, is marked with a solid green dot. It is labelled z. The disc is shaded blue. Between the left-hand and right-hand diagrams is a curved arrow pointing from left to right. Above it is the label f. On the right-hand diagram the point f of alpha is marked with a solid black dot and labelled. A circular disc is drawn with the point f of alpha as its centre and a solid black circle as its boundary. This disc has radius approximately 50% greater than the radius of the disc surrounding the point alpha in the left-hand diagram. Inside the disc a second point, above and to the right of the point f of alpha, is marked with a solid green dot and labelled f of z. The disc is shaded blue. Outside the disc, above it and slightly to the left, is the text, scale by the modulus of f prime of alpha. Outside the disc, diametrically opposite the first text, is a curved arrow parallel to the circular boundary of the disc, which points in an anticlockwise direction. Next to it is the text, rotate by Arg f prime of alpha.