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Session 1: Differentiation

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This figure consists of two copies of the complex plane, arranged side by side. The axes are not labelled. On the left-hand diagram, a bold vertical line, drawn in black, passes through an arbitrary point on the positive horizontal axis. It is marked with a direction arrow pointing upwards, and labelled capital gamma sub 1. A bold horizontal line, drawn in blue, passes through an arbitrary point on the positive vertical axis. It is marked with a direction arrow pointing to the right, and labelled capital gamma sub 2. The two bold lines intersect at right angles in the upper-right quadrant. Between the two copies of the complex plane is a curved horizontal arrow pointing from left to right. It is labelled f of z equals z bar. On the right-hand diagram, a bold vertical line, drawn in black, passes through the same arbitrary point on the positive horizontal axis. It is marked with a direction arrow pointing downwards, and labelled f of capital gamma sub 1. A bold horizontal line, drawn in blue, passes through a point on the negative vertical axis. (This point is the same distance below the origin as the point used on the vertical axis in the left-hand diagram was above it.) The horizontal line is marked direction arrow pointing to the right, and labelled f of capital gamma sub 2. The two bold lines intersect at right angles in the lower-right quadrant.