Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
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Problem 1
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 − 4i)Problem 1
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 = 3 − 5t, y = 4 + 2t; t = 1Problem 1
In Exercises 1–10, perform the indicated operations and write the result in standard form. (8 − 3i) − (17 − 7i)Problem 1
In Exercises 1–3, perform the indicated operations and write the result in standard form. (6 − 7i)(2 + 5i)Problem 1
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, 225°)Problem 2
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 = 7 − 4t, y = 5 + 6t; t = 1Problem 2
In Exercises 1–3, perform the indicated operations and write the result in standard form. 5 / 2−iProblem 3
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (3 + 2i) − (5 − 7i)Problem 3
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 = t² + 1, y = 5 − t³; t = 2Problem 3
In Exercises 1–3, perform the indicated operations and write the result in standard form. ___ ___ 2√−49 + 3√−64Problem 3
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, 5π/4)Problem 4
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 = t² + 3, y = 6 − t³; t = 2Problem 4
In Exercises 1–10, perform the indicated operations and write the result in standard form. (3 − 4i)²Problem 5
In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 − (−5 + 4i) − (−13 − i)Problem 5
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 = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2Problem 5
In Exercises 1–10, perform the indicated operations and write the result in standard form. (7 + 8i)(7 − 8i)Problem 5
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, π)Problem 6
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 = 2 + 3 cos t, y = 4 + 2 sin t; t = πProblem 6
In Exercises 1–10, perform the indicated operations and write the result in standard form. 6 / 5+iProblem 7
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 = 2Problem 7
In Exercises 1–10, perform the indicated operations and write the result in standard form. 3+4i / 4−2iProblem 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 8
In Exercises 1–10, perform the indicated operations and write the result in standard form. ___ ___ √−32 − √−18Problem 9
In Exercises 1–10, perform the indicated operations and write the result in standard form. ___ (−2 + √−100)²Problem 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 θProblem 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 10
In Exercises 1–10, perform the indicated operations and write the result in standard form. __ 4 + √−8 / 2Problem 11
In Exercises 9–20, find each product and write the result in standard form. (−5 + 4i)(3 + i)