Consider a point P moving in the complex plane in a counterclockwise direction around a circle...

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Consider a point P moving in the complex plane in a counterclockwise direction around a circle of radius one and center at the origin. Describe what happens to the image of P under the complex mapping w = z^5 as P makes one full revolution around the circle. Consider a point P moving in the complex plane in a counterclockwise direction around a circle of radius one and center at the origin. Describe what happens to the image of P under the complex mapping w = z^5 as P makes one full revolution around the circle.

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Lets first consider what happens to a point on the unit circle as it moves counterclockwise around t... View the full answer