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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. The left-hand copy shows a circle centred at the origin. An arbitrary point on the circle in the upper-right quadrant is labelled alpha and marked with a solid blue dot. A sequence of points on the circumference starts in the upper-left quadrant and approaches the point alpha at decreasing intervals. The first four points in the sequence are marked with solid black dots. An ellipsis between the fourth point and the point alpha indicates that the sequence of points continues indefinitely getting closer to alpha. Above the sequence of points is a curved arrow pointing from left to right. It is labelled: open bracket, z sub n, close bracket. The right-hand copy of the complex plane shows the same circle centred at the origin, and the same arbitrary point alpha on the circle is labelled and marked with a solid blue dot. A sequence of points outside the circle approaches the point alpha at decreasing intervals along the normal to the circle at alpha. The first three points in the sequence are marked with solid black dots. An ellipsis between the third point and the point alpha indicates that the sequence of points continues indefinitely getting closer to alpha. An arrow directed towards alpha is drawn outside the circle parallel to the sequence of points. It is labelled: open bracket, z prime sub n, close bracket.