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A plane is flying in the direction \(200^{\circ}\) with an air speed of \(500 \mathrm{mph}\). Its course and ground speed are \(210^{\circ}\) and \(450 \mathrm{mph}\) respectively. What are the direction and speed of the wind?

A river flows from east to west. A swimmer on the south bank wants to swim to a point on the opposite shore directly north of her starting point. She can swim at \(2.8 \mathrm{mph},\) and there is a 1 -mph current in the river. In what direction should she head so as to travel directly north (that is, what angle should her path make with the south bank of the river)?

Describe what happens geometrically when you multiply a complex number by 2.