Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
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- In Exercises 1–8, add or subtract as indicated and write the result in standard form. 8i − (14 − 9i)
Problem 7
- In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = (60 cos 30°)t, y = 5 + (60 sin 30°)t − 16t²; t = 2
Problem 7
- In Exercises 1–10, perform the indicated operations and write the result in standard form. 3+4i / 4−2i
Problem 7
- In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, −135°)
Problem 7
- In Exercises 1–10, perform the indicated operations and write the result in standard form. ___ ___ √−32 − √−18
Problem 8
- In Exercises 1–10, perform the indicated operations and write the result in standard form. ___ (−2 + √−100)²
Problem 9
- In Exercises 9–20, find each product and write the result in standard form. −3i(7i − 5)
Problem 9
- In Exercises 7–12, test for symmetry with respect to a. the polar axis. b. the line θ=π2. c. the pole. r = 4 + 3 cos θ
Problem 9
- In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (−3, −3π/4)
Problem 9
- In Exercises 1–10, perform the indicated operations and write the result in standard form. __ 4 + √−8 / 2
Problem 10
- In Exercises 9–20, find each product and write the result in standard form. (−5 + 4i)(3 + i)
Problem 11
- In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = t − 2, y = 2t + 1; −2 ≤ t ≤ 3
Problem 11
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (2, 45°)
Problem 11
- Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of θ.
Problem 11
- In Exercises 9–20, find each product and write the result in standard form. (7 − 5i)(−2 − 3i)
Problem 13
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (3, 90°)
Problem 13
- In Exercises 13–14, graph each polar equation. r = 1 + sin θ
Problem 13
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 cos θ
Problem 13
- In Exercises 15–16, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. _ x = √t , y = t + 1; −∞ < t < ∞
Problem 15
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (3, 4π/3)
Problem 15
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − sin θ
Problem 15
- In Exercises 9–20, find each product and write the result in standard form. (−5 + i)(−5 − i)
Problem 17
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−1, π)
Problem 17
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 + 2 cos θ
Problem 17
- In Exercises 9–20, find each product and write the result in standard form. (2 + 3i)²
Problem 19
- In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ < t < ∞
Problem 19
- In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−2, − π/2)
Problem 19
- In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 + cos θ
Problem 19
- In Exercises 21–28, divide and express the result in standard form. 2 / 3 - i
Problem 21
- 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
Problem 21