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We realize S as the unit circle |z| = 1 in the complex plane C. (a) Check that the formula f : z z

We realize S as the unit circle |z| = 1 in the complex plane C. (a) Check that the formula f : z z is a map from S to S. (i.e. that you are getting points on S.) (b) Show that this map is smooth (by using local coordinates for the circle).

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