Jeopardy! for the Classroom. Real Numbers Complex Numbers Polar Equations Polar Graphs Operations w/ Complex Numbers C & V 100 200 300 400 500.

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Presentation transcript:

Jeopardy! for the Classroom

Real Numbers Complex Numbers Polar Equations Polar Graphs Operations w/ Complex Numbers C & V

The polar form of (-3,0)

What is (3, π) or (3, 180°)?

The rectangular form of (-2, 3π/2)

What is (0, 2)?

The exact rectangular form of (4, -5π/6)

What is (-2√3, -2)?

The exact polar form of (-3, 3)

What is (3√2, 135°)?

The rectangular form of (-5, π/10)

What is (-4.76, -1.55)?

The exact polar form of 1 - i

What is √2(cos 315°+ i sin 315°)?

The exact polar form of -1 + √3i

What is 2(cos 120° + i sin 120°)?

The exact rectangular form of 6(cos 4π/3 + i sin 4π/3)

What is (-3, -3√3)?

The rectangular form of 5(cos 3π/5 + i sin 3π/5)

What is (-1.55, 4.76)?

The polar form of -4

What is 4(cos π + i sin π)?

The rectangular form of r cos Θ = 2

What is x = 2?

The polar form of x 2 + y 2 = 9

What is r = 3?

The rectangular form of r = - 7 sin Θ

What is x 2 + y 2 = -7y?

The polar form of y = -√3 x

What is Θ = 2π/3?

The rectangular form of r sec Θ = 3

What is x 2 + y 2 = 3x?

The center and radius of r = -2 sin Θ

What are (0, -1) and 1?

The position of the first petal of r = 3 sin 3Θ

What is 30°?

The shape of the graph of r = 4 – 4 sin Θ

What is a cardioid?

The number of petals on the graph of r 2 = 4 sin 2Θ

What is two?

The shape of the graph of r = 3 – 4 cos Θ

What is a limaçon with a loop?

The number of complex roots of -32i 1/5

What is five?

z·w if z = 2(cos 50°+ i sin 50°) w = 3(cos 160° + i sin 160°)

What is 6(cos 210° + i sin 210°)?

Daily Double

The standard form a + bi of [5(cos 2π/3 + i sin 2π/3)] 3

What is 125?

z/w in rectangular form if z = 3(cos 40°+ i sin 40°) w = 6(cos 160° + i sin 160°)

What is -1/4 - √3/4 i?

The complex cube roots of -2 – 2i

What are √2(cos 75° + i sin 75°) √2(cos 195° + i sin 195°) √2(cos 315° + i sin 315°)?

The letters used to represent polar coordinates

What are r and Θ?

The name of the origin in polar coordinates

What is the pole?

The name of the graph that is shaped like a propeller

What is a lemniscate?

The name of the distance from the origin to the point representing a complex number

What is the magnitude or modulus?

The theorem that is used to raise a complex number to a power

What is DeMoivre’s?

Final Jeopardy!

Concepts and Vocabulary

The difference between rectangular and polar coordinates

What is measuring a horizontal and vertical distance from the origin vs. measuring an angle made with the polar axis and a distance from the pole?