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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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Which of the following complex numbers is represented by the point J?
  1. [math]8 \ (cos180° + i sin180°)[/math]
  2. [math]8 \ (cos0° + i sin0° )[/math]
  3. [math]64 \ (cos(180° + i sin180°)[/math]
  4. [math]-8 \ (cos0° + i sin0°)[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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Which of the following points represents the complex number [math]sqrt(106) \ ( \ cos(-119.1°) + i sin(-119.1°) \ ) ?[/math]
  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 [math]5 \ (cos126.9° + i sin126.9°) ?[/math]
  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. [math]8 \ [ \ cos(-90°) + i sin(-90°) \ ][/math]
  2. [math] 9sqrt(2) \ [ \ cos(45°) + i sin(45°) \ ] [/math]
  3. [math]sqrt(13) \ [ \ cos(-33.7°) + isin(-33.7°) \ ] [/math]
  4. [math]4sqrt(5) \ [ \ cos(-46.6°) + isin(-46.6°) \ ] [/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert [math]-4+2i[/math] to polar form.
  1. [math] 2sqrt(5) \ [ \ cos(153.4°) + i sin(153.4°) \ ] [/math]
  2. [math] 2sqrt(3) \ [ \ cos(153.4°) + i sin(153.4°) \ ] [/math]
  3. [math] 2 sqrt(5) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ][/math]
  4. [math] 2sqrt(3) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ] [/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert [math]3sqrt(7) \ (cos80° + i sin80°)[/math] to rectangular form.
  1. [math]7.8 + 1.4i[/math]
  2. [math]1.4 + 1.0 i[/math]
  3. [math]1.4 + 7.8i[/math]
  4. [math]0.2 + 1.0i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
What is the rectangular form of the complex number whose polar coordinates are [math](6, -18°) ?[/math]
  1. [math]5.7 - 0.3 i[/math]
  2. [math]5.7 - 1.9i[/math]
  3. [math]5.7 + 1.9i[/math]
  4. [math]1.9 - 5.7i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
What is the polar form of the complex number [math]-5 ?[/math]
  1. [math] -5 \ (cos180° + i sin180°)[/math]
  2. [math]5 \ (cos0° + i sin0°)[/math]
  3. [math]5 \ (cos180° + isin180°)[/math]
  4. [math]"This is not a complex number."[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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What is the distance from I to the origin? Let [math]alpha[/math] represent this value.
  1. [math]alpha = 5[/math]
  2. [math]alpha = 2sqrt(5)[/math]
  3. [math]alpha = 4[/math]
  4. [math]alpha = 3[/math]
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 [math]beta[/math] represent this angle.
  1. [math]beta = 45.0°[/math]
  2. [math]beta = 53.1°[/math]
  3. [math]beta = 36.9°[/math]
  4. [math]beta = 48.6°[/math]
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. [math]6 - 7i[/math]
  2. [math]-7 -7i[/math]
  3. [math]-7 + 6i[/math]
  4. [math]6+6i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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What are the polar coordinates of the complex number [math]z ?[/math]
  1. [math] (4, 30.2°)[/math]
  2. [math] (5, 36.9°)[/math]
  3. [math] (5, 53.1°)[/math]
  4. [math] (4, 53.1°)[/math]
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. [math]7 - 6i[/math]
  2. [math]-6 + 7i[/math]
  3. [math]-6 - 6i[/math]
  4. [math]-7 - 6i[/math]
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 [math]alpha[/math] represents the modulus of [math]z[/math], and [math]beta[/math] represents the argument of [math]z.[/math]
  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 [math]3 - 2i ?[/math]
  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 [math]-5 + 9i ?[/math]
  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. [math]8[/math]
  2. [math]9 + 9i[/math]
  3. [math]-3 + 4i[/math]
  4. [math]-7 -7i[/math]
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