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Common Core Standard HSN-CN.B.4 Questions

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

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Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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What is the distance from I to the origin? Let α represent this value.
  1. α=5
  2. α=2√5
  3. α=4
  4. α=3
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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If a line is drawn between I and the origin, what is the angle between this line and the positive x-axis, starting from the x-axis and going in a counterclockwise direction? Let β represent this angle.
  1. β=45.0°
  2. β=53.1°
  3. β=36.9°
  4. β=48.6°
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers is represented by point A?
  1. 6-7i
  2. -7-7i
  3. -7+6i
  4. 6+6i
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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What are the polar coordinates of the complex number z?
  1. (4,30.2°)
  2. (5,36.9°)
  3. (5,53.1°)
  4. (4,53.1°)
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers is represented by point B?
  1. 7-6i
  2. -6+7i
  3. -6-6i
  4. -7-6i
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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What is the significance of the answers in parts a and b compared to part c? Choose the best answer.
  1. They are similar, since the geometry of the complex plane is closely related to the polar coordinates of a complex number.
  2. They are the same. This is only a phenomenon of the first quadrant though; for a complex number in any other quadrant, these values would be different.
  3. They are the same, since α represents the modulus of z, and β represents the argument of z.
  4. Any similarity or equality is pure chance; there is no relationship between these values.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following points represents the complex number 3-2i?
  1. E
  2. I
  3. A
  4. This number is not represented by any point given.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following points represents the complex number -5+9i?
  1. E
  2. B
  3. L
  4. This number is not represented by any point given.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers does not have a corresponding point shown on the given graph?
  1. 8
  2. 9+9i
  3. -3+4i
  4. -7-7i
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers is represented by the point C?
  1. √85 (cos49.4°+isin49.4°)
  2. 7 (cos45°+isin45°)
  3. √85 (cos40.6°+isin40.6°)
  4. 6 (cos45°+isin45°)
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers is represented by the point J?
  1. 8 (cos180°+isin180°)
  2. 8 (cos0°+isin0°)
  3. 64 (cos(180°+isin180°)
  4. -8 (cos0°+isin0°)
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following points represents the complex number √106 ( cos(-119.1°)+isin(-119.1°) )?
  1. D
  2. L
  3. J
  4. This number is not represented by any given point.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following points represents the complex number 5 (cos126.9°+isin126.9°)?
  1. A
  2. I
  3. E
  4. This number is not represented by any given point.
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following complex numbers does not have a corresponding point shown on the given graph?
  1. 8 [ cos(-90°)+isin(-90°) ]
  2. 9√2 [ cos(45°)+isin(45°) ]
  3. √13 [ cos(-33.7°)+isin(-33.7°) ]
  4. 4√5 [ cos(-46.6°)+isin(-46.6°) ]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert -4+2i to polar form.
  1. 2√5 [ cos(153.4°)+isin(153.4°) ]
  2. 2√3 [ cos(153.4°)+isin(153.4°) ]
  3. 2√5 [ cos(-26.6°)+isin(-26.6°) ]
  4. 2√3 [ cos(-26.6°)+isin(-26.6°) ]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert 3√7 (cos80°+isin80°) to rectangular form.
  1. 7.8+1.4i
  2. 1.4+1.0i
  3. 1.4+7.8i
  4. 0.2+1.0i
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
What is the rectangular form of the complex number whose polar coordinates are (6,-18°)?
  1. 5.7-0.3i
  2. 5.7-1.9i
  3. 5.7+1.9i
  4. 1.9-5.7i
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