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문제 1
In Exercises 1–10, perform the indicated operations and write the result in standard form. (8 − 3i) − (17 − 7i)
문제 4
In Exercises 1–10, perform the indicated operations and write the result in standard form. (3 − 4i)²
문제 5
In Exercises 1–10, perform the indicated operations and write the result in standard form. (7 + 8i)(7 − 8i)
문제 5.RE.61
In Exercises 61–63, test for symmetry with respect to
a. the polar axis.
b. the line θ = π/2.
c. the pole.
r = 5 + 3 cos θ
문제 5.RE.65
In Exercises 64–70, graph each polar equation. Be sure to test for symmetry. r = 2 + 2 sin θ
문제 5.RE.57
In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system. r = 5 csc θ
문제 5.RE.55
In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system. θ = 3π/4
문제 6
In Exercises 1–10, perform the indicated operations and write the result in standard form. 6 / 5+i
문제 7
Perform the indicated operations and write the result in standard form. 3+4i / 4−2i
문제 8
Perform the indicated operations and write the result in standard form. √−32 − √−18
문제 9
Perform the indicated operations and write the result in standard form. (−2 + √−100)²
문제 10
Perform the indicated operations and write the result in standard form. (4 + √−8 )/ 2
문제 11
In Exercises 11–14, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. 1 − i
문제 15
Write each complex number in rectangular form. If necessary, round to the nearest tenth. 8(cos 60° + i sin 60°)
문제 17
In Exercises 15–18, write each complex number in rectangular form. If necessary, round to the nearest tenth. 6 (cos 2π/3 + i sin 2π/3)
문제 19
In Exercises 19–21, find the product of the complex numbers. Leave answers in polar form.
z₁ = 3(cos 40°+i sin 40°)
z₂ = 5(cos 70°+i sin 70°)
문제 23
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)
문제 25
In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 20° + i sin 20°)]³
문제 27
In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [1/2 (cos π/14 + i sin π/14)]⁷
문제 28
In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ (1−i√3)²
문제 29
In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (−2 − 2i)⁵
문제 31
In Exercises 30–31, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 125(cos 165° + i sin 165°)
문제 32
In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex fourth roots of 16 (cos 2π/3 + i sin 2π/3)
문제 33
In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex cube roots of 8i
문제 34
In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex cube roots of −1
문제 35
In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex fifth roots of −1 − i
문제 71
In Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = 2t − 1, y = 1 − t; −∞ < t < ∞
문제 75
In Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = 3 + 2 cos t, y = 1+2 sin t; 0 ≤ t < 2π
문제 77
Find two different sets of parametric equations for y = x² + 6.