The Complex Number System
HSN-CN.B.5
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- 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 polar forms of a given complex number represent the same number.
- HSN-CN.B.5(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)^{3} = 8 because (-1 + √3 i) has modulus 2 and argument 120°.
- HSN-CN.B.6(+) 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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HSN-CN.B.5
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)^{3} = 8 because (-1 + √3 i) has modulus 2 and argument 120°.
12 Lesson(s)
Complex Addition
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
The lowly parallelogram helps students make sense of addition and subtraction of complex numbers.
Standards:
Favorites
(2)
Resources
(18)
Reflections
(2)
Trigonometric Form of Complex Numbers
12th Grade Math »
Unit: Additional Trigonometry Topics
12th Grade Math »
Unit: Additional Trigonometry Topics
Big Idea:
Complex numbers can be represented on a graph?!
Standards:
Favorites
(2)
Resources
(10)
Reflections
(1)
De Moivre's Theorem
12th Grade Math »
Unit: Additional Trigonometry Topics
12th Grade Math »
Unit: Additional Trigonometry Topics
Big Idea:
How did mathematicians raise numbers to high powers before there were calculators?
Standards:
Favorites
(1)
Resources
(11)
Reflections
(1)
Unit Review: Additional Trigonometry Topics
12th Grade Math »
Unit: Additional Trigonometry Topics
12th Grade Math »
Unit: Additional Trigonometry Topics
Big Idea:
Give your students time to grapple with the important concepts of this unit.
Standards:
Favorites
(1)
Resources
(6)
The Parallelogram Rule
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
A graphical context makes arithmetic with complex numbers more meaningful and concrete.
Standards:
Favorites
(2)
Resources
(11)
Reflections
(1)
Complex Arithmetic and Vectors
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Recognizing an application for complex numbers - vector addition - helps to give them meaning.
Standards:
Favorites
(1)
Resources
(7)
Multiplying Complex Numbers, Day 4 of 4
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Practice helps students uncover hidden patterns and discover simple rules.
Standards:
Favorites
(1)
Resources
(9)
Muliplying Complex Numbers, Day 3 of 4
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Practice helps students uncover hidden patterns and discover simple rules.
Standards:
Favorites
(1)
Resources
(11)
Complex Numbers and Trigonometry
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
How is it possible to write a complex number using trigonometric functions?
Standards:
Resources
(23)
Reflections
(3)
DeMoivre's Theorem
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
If I know how to multiply complex numbers how can I find powers of complex numbers?
Standards:
Resources
(9)
Roots of Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
How can find the nth roots of a complex number?
Standards:
Resources
(15)
Reflections
(1)
Review
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
Through graphic organizers students will review ideas of vectors and complex numbers.
Standards:
Resources
(3)
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