If a golfer tees off with an initial velocity of *v*_{0} feet per second and an initial angle of trajectory *θ*, we can describe the position of the ball (*x*, *y*) with *parametric equations*. Parametric equations are a set of equations that express a set of quantities, such as *x*- and *y*-coordinates, as explicit functions of a number of independent variables, known as *parameters.* At some time *t* (seconds), the horizontal distance *x* (feet), from the golfer down the fairway, and the height above the ground *y* (feet) are given by the parametric equations:

*x* = (*v*_{0} cos *θ*)*t* and *y* = (*v*_{0} sin *θ*)*t* − 16*t*^{2}

where we have neglected air resistance, and *t* is the parameter. These *parametric equations* essentially map the path of the ball over time.

IN THIS CHAPTER, we will review complex numbers. We will discuss the polar (trigonometric) form of complex numbers and operations on complex numbers. We will then introduce the polar coordinate system, which is often a preferred coordinate system over the rectangular system. We will graph polar equations in the polar coordinate system and finally discuss parametric equations and their graphs.

LEARNING OBJECTIVES

Perform operations on complex numbers.

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