Podcast
Questions and Answers
What is the unit of measurement used for the graphic in the complex plane?
What is the unit of measurement used for the graphic in the complex plane?
1 cm
What is the center and angle of rotation for r1?
What is the center and angle of rotation for r1?
Center: 0, Angle: π/3
What is the equation being solved in part A, question 1?
What is the equation being solved in part A, question 1?
3y = 5(15-x)
What is the name of the circle being referenced in part A, question 2?
What is the name of the circle being referenced in part A, question 2?
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What is the symbol used to represent the distance traveled by the point A on the circle ζ?
What is the symbol used to represent the distance traveled by the point A on the circle ζ?
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What is the distance traveled by point A when it undergoes a rotation r1?
What is the distance traveled by point A when it undergoes a rotation r1?
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What is the goal of question 3 in Part A?
What is the goal of question 3 in Part A?
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What is the name of the homothety with center O and ratio 4?
What is the name of the homothety with center O and ratio 4?
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What are the symbols used to represent the homothety of h1 and h2 on the circleζ?
What are the symbols used to represent the homothety of h1 and h2 on the circleζ?
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What is the composition of s1, m being a natural number?
What is the composition of s1, m being a natural number?
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What is the formula for calculating the composition of s1, m times, followed by s2, n times?
What is the formula for calculating the composition of s1, m times, followed by s2, n times?
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What is the center of the direct similitude 'f'?
What is the center of the direct similitude 'f'?
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Study Notes
Complex Plane
- Complex plane uses an orthonormal direct coordinate system (0,i,j) with a unit of 1 cm.
- Rotation r₁: center O, angle π/3
- Rotation r₂: center O, angle π/5
Part A
- Equation: 3y = 5(15 - x) where x and y are integers.
- Point I has an affix of 1.
- Point A moves on the unit circle (ζ) centered at O, starting at I.
- Distance A travels after p rotations of r₁ and q rotations of r₂ is calculated in cm.
- Rotation r₁ covers a distance of π/3 cm.
- Rotation r₂ covers a distance of π/5 cm.
- Find integer values of p and q such that A travels exactly 2.5 times around the unit circle.
Part B
- Homothétie h₁: center O, ratio 4
- Homothétie h₂: center O, ratio -6
- Define s₁ = r₁ ◦ h₁ and s₂ = r₂ ◦ h₂.
- Find the nature and characteristics of s₁ and s₂.
- Define composite s₁ ◦ s₁... ◦s₁ (m times) = Sm
- Define composite s₂ ◦ s₂... ◦s₂ (n times) = Sn
- Define f = Sm ◦ Sn
- Prove f is a direct similarity with center O, ratio 2^2m × 3^n, and angle (mπ/3 + nπ/5)
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Description
Test your understanding of the complex plane and transformations with this quiz. Part A focuses on rotations and distances along the unit circle, while Part B delves into homothety and composite transformations. Solve equations and prove properties related to direct similarity.
