In Exercises 21–28, divide and express the result in standard form.


3 / 4+i

In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = t, y = 2t

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 − 3 sin θ

In Exercises 22–24, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form.

z₁ = 5 (cos 4π/3 + i sin 4π/3)

z₂ = 10 (cos π/3 + i sin π/3)

In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. −3 + 4i

In Exercises 21–28, divide and express the result in standard form. 2 / 3 - i

In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which

a. r>0, 2π < θ < 4π.

b. r<0, 0. < θ < 2π.

c. r>0, −2π. < θ < 0.

(5, π/6)