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
What this standard means
Students need to treat complex numbers as points on a coordinate plane. They find the distance between two complex numbers by subtracting them, then finding the modulus of the result. They find a midpoint by averaging the real parts and averaging the imaginary parts.
Mastery looks like moving smoothly between a + bi, ordered pairs, and a graph. Students can explain why the distance formula and midpoint formula still work. Common snags are subtracting in the wrong order, dropping the i, mixing real and imaginary parts, and thinking modulus means only absolute value on a number line.
Ways to teach it
- Have students plot two complex numbers on graph paper, draw the segment, then calculate its length using the modulus of their difference.
- Ask students to explain why averaging two complex numbers gives the midpoint, using both a graph and algebra.
- Give an exit ticket with two complex numbers and ask for the distance, midpoint, and one sentence explaining each method.
- Connect to map coordinates by treating real and imaginary parts like east-west and north-south directions for two drone locations.
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Related standards
- CCSS.Math.Content.HSN-CN.B.4
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and pol...
- CCSS.Math.Content.HSN-CN.A.3
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- CCSS.Math.Content.HSN-CN.B
Represent complex numbers and their operations on the complex plane.
- CCSS.Math.Content.HSN-CN.B.5
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representatio...