CCSS.Math.Content.HSN-CN.B.6
The Standard
(+) 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.
Common Core State Standards for Mathematics · The Complex Number System
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students treat complex numbers as points with real and imaginary coordinates. They subtract coordinates to find the segment length and average corresponding coordinates to locate the halfway point.
What Mastery Looks Like
- A student correctly finds the horizontal and vertical changes, then uses them to calculate segment length. The student averages both coordinate parts and writes the midpoint as a complex number.
Common Misconceptions
- Students may add the endpoints when finding distance or forget to take the square root. They may average only the real parts. Some confuse a complex number's modulus with the distance between two points.
How to Assess It
- Exit ticket: For endpoints 2 + 3i and -4 + i, find the distance and midpoint. Ask students to show each calculation.
Lesson moves
Ways to Teach It
Plot two complex numbers on a coordinate grid, connect them with string, measure the segment, then verify the distance and midpoint algebraically.
Write an explanation for why distance uses subtraction before modulus, while a midpoint averages real parts and imaginary parts separately.
Run a card match with endpoint pairs, difference vectors, distances, and midpoints, requiring students to justify every completed set.
Model two drone locations as complex numbers, then calculate their separation and the coordinates of a halfway meeting point.
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Printable HSN-CN.B.6 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-CN.B.6, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-CN.B.4
Plotting complex numbers as plane points supports interpreting differences as vectors for distance and averages as midpoint coordinates.
- CCSS.Math.Content.HSN-CN.A.3
Finding moduli of complex numbers supports calculating distance as the modulus of a difference in the complex plane.
- CCSS.Math.Content.8.G.B.8
Coordinate-plane distance using horizontal and vertical changes carries over directly to modulus of a complex difference.
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