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문제 67
In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 8(cos 210° + i sin 210°)
문제 68
In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 27(cos 306° + i sin 306°)
문제 69
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fourth roots of 81 (cos 4π/3 + i sin 4π/3)
문제 70
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of 32 (cos 5π/3 + i sin 5π/3)
문제 71
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of 32
문제 72
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 64
문제 73
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 1
문제 75
In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 1 + i
문제 79
In Exercises 77–80, convert to polar form and then perform the indicated operations. Express answers in polar and rectangular form.
(1 + i√3)(1 − i)) / 2√3 − 2i
문제 81
In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangular form. x⁶ − 1 = 0
문제 83
In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangular form.
x⁴ + 16i = 0
문제 85
In Exercises 81–86, solve each equation in the complex number system. Express solutions in polar and rectangular form.
x³ − (1 + i√3) = 0
문제 87
In calculus, it can be shown that e^(iθ) = cos θ + i sin θ. In Exercises 87–90, use this result to plot each complex number. e^(πi/4)
문제 89
In calculus, it can be shown that e^(iθ) = cos θ + i sin θ. In Exercises 87–90, use this result to plot each complex number. -e^-πi
문제 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°)
문제 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)
문제 5.3.53
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x² + y² = 9
문제 5.3.56
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
x² + (y + 3)² = 9
문제 5.3.59
In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. r = 8
문제 5.3.52
Convert each rectangular equation to a polar equation that expresses r in terms of θ.
y = 3
문제 5.3.51
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x = 7
문제 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)
문제 5.3.55
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. (x − 2)² + y² = 4
문제 5.3.49
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. 3x + y = 7
문제 5.3.57
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
y² = 6x
문제 5.3.65
In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. r = 4 csc θ
문제 5.3.47
In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. (5, 0)
문제 5.3.54
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
x² + y² = 16
문제 5.3.58
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
x² = 6y
문제 5.3.45
In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. (−√3,−1)