Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
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- In Exercises 37–52, perform the indicated operations and write the result in standard form. __ (−2 + √−4)²
Problem 41
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. (−2, 2)
Problem 41
- In Exercises 37–52, perform the indicated operations and write the result in standard form. __ (−3 − √−7)²
Problem 43
- In Exercises 41–48, the rectangular coordinates of a point are given. Find polar coordinates of each point. Express θ in radians. _ (2,−2√3)
Problem 43
- In Exercises 35–44, test for symmetry and then graph each polar equation. r = 2 + 3 sin 2θ
Problem 43
- In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ −8 + √−32 / 24
Problem 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)
Problem 45
- In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ −5 − √−12 / 48
Problem 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)
Problem 47
- In Exercises 37–52, perform the indicated operations and write the result in standard form. __ __ _ √−8 (√−3 − √5 )
Problem 49
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. 3x + y = 7
Problem 49
- In Exercises 37–52, perform the indicated operations and write the result in standard form. __ ___ (3√−5 )( −4√−12 )
Problem 51
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x = 7
Problem 51
Problem 52
Convert each rectangular equation to a polar equation that expresses r in terms of θ.
y = 3
- In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. (2 − 3i)(1 − i) − (3 − i)(3 + i)
Problem 53
- In Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = 4x − 3
Problem 53
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. x² + y² = 9
Problem 53
Problem 54
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
x² + y² = 16
- In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ. (x − 2)² + y² = 4
Problem 55
- In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. (2 + i)² − (3 − i)²
Problem 55
- In Exercises 53–56, find two different sets of parametric equations for each rectangular equation. y = x² + 4
Problem 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
Problem 55
Problem 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
- In Exercises 53–58, perform the indicated operation(s) and write the result in standard form. ___ ___ 5√−16 + 3√−81
Problem 57
- In Exercises 57–58, the parametric equations of four plane curves are given. Graph each plane curve and determine how they differ from each other. x = t and y = t² − 4
Problem 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
Problem 57
Problem 58
In Exercises 49–58, convert each rectangular equation to a polar equation that expresses r in terms of θ.
x² = 6y
- Evaluate x² − 2x + 2 for x = 1 + i.
Problem 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
Problem 59
- Evaluate x²+19 / 2−x for x = 3i.
Problem 61