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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 $alpha$ represent this value.
1. $alpha = 5$
2. $alpha = 2sqrt(5)$
3. $alpha = 4$
4. $alpha = 3$
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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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 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 $alpha$ represents the modulus of $z$, and $beta$ 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. $sqrt(85) \ (cos49.4° + i sin49.4°)$
2. $7 \ (cos45° + i sin45°)$
3. $sqrt(85) \ (cos40.6° + i sin40.6°)$
4. $6 \ (cos45° + i sin45°)$
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. $8 \ (cos180° + i sin180°)$
2. $8 \ (cos0° + i sin0° )$
3. $64 \ (cos(180° + i sin180°)$
4. $-8 \ (cos0° + i sin0°)$
Grade 11 Complex Numbers CCSS: HSN-CN.B.4

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

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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. $8 \ [ \ cos(-90°) + i sin(-90°) \ ]$
2. $9sqrt(2) \ [ \ cos(45°) + i sin(45°) \ ]$
3. $sqrt(13) \ [ \ cos(-33.7°) + isin(-33.7°) \ ]$
4. $4sqrt(5) \ [ \ cos(-46.6°) + isin(-46.6°) \ ]$
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert $-4+2i$ to polar form.
1. $2sqrt(5) \ [ \ cos(153.4°) + i sin(153.4°) \ ]$
2. $2sqrt(3) \ [ \ cos(153.4°) + i sin(153.4°) \ ]$
3. $2 sqrt(5) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ]$
4. $2sqrt(3) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ]$
Grade 11 Complex Numbers CCSS: HSN-CN.B.4
Convert $3sqrt(7) \ (cos80° + i sin80°)$ to rectangular form.
1. $7.8 + 1.4i$
2. $1.4 + 1.0 i$
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. $5.7 - 0.3 i$
2. $5.7 - 1.9i$
3. $5.7 + 1.9i$
4. $1.9 - 5.7i$
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