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Common Core Standard HSN-CN.B.6 Questions

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

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Grade 11 Complex Numbers CCSS: HSN-CN.B.6
Let [math]z=-8+5i[/math]. If the midpoint of the line segment created by complex numbers [math]z[/math] and [math]w[/math] is [math]-3+3/2 i[/math], what is the value of [math]w ?[/math]
  1. [math]w = -11/2 + 13/4 i[/math]
  2. [math]w = 2-2i[/math]
  3. [math]w = 14 + i[/math]
  4. [math]w = 4 + 7/2 i[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
Find the distance between [math]z = 6 + 7i[/math] and [math]w = -2 - 3i[/math] in the complex plane.
  1. [math]4sqrt(2)[/math]
  2. [math]18[/math]
  3. [math]2sqrt(2)[/math]
  4. [math]2sqrt(41)[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
Which of the following expressions represent(s) the distance between [math]z_1[/math] and [math]z_2[/math] in the complex plane? Choose all correct answers.
  1. [math]|z_1 - z_2|[/math]
  2. [math]|z_2 - z_1|[/math]
  3. [math]|z_2| - |z_1|[/math]
  4. [math]|z_2 + z_1|[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
What is the distance between the complex numbers [math]2-4i[/math] and [math]-3/2 - 1/2 i[/math] in the complex plane?
  1. [math]7/2 sqrt(2)[/math]
  2. [math]1/2sqrt(130)[/math]
  3. [math]5/2 sqrt(2)[/math]
  4. [math]1/8 sqrt(82)[/math]
Grade 11 Complex Numbers CCSS: HSN-CN.B.6
Kayslee is given the complex numbers C and J in polar form, [math]2sqrt(5) \ (cos(63.4° + i sin63.4°)[/math] and [math] sqrt(2) \ (cos(135° + isin135°)[/math] respectively. She notices that she can find the distance between these numbers, [math]d[/math], in the complex plane simply by taking the difference of their arguments, [math]71.6°[/math], and then applying the law of cosines formula, [math] d = sqrt( (2sqrt(5))^2 + (sqrt(2))^2 - 2 * 2sqrt(5) * sqrt(2) cos71.6° )[/math]. Is this value correct? Check using the method for complex numbers in rectangular form. Is Kayslee's method applicable to any two complex numbers in the complex plane?
Coordinate Plane - 5x5 - With Dots
  1. Yes, the value is correct, and Kayslee's method will work for all complex numbers (being careful with how the difference of arguments is calculated).
  2. Yes, the value is correct, but this method only works in some instances.
  3. Yes, the value is correct, but this is merely coincidence (there is no reason for it).
  4. No, this value is not correct, and her method is also not correct (it does not correctly calculate the distance between complex numbers in the complex plane).

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