The Complex Number System
HSN-CN.B.4
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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.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.
11 Lesson(s)
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)
Inconceivable! The Origins of Imaginary Numbers
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Imaginary numbers aren't any more imaginary than negative numbers!
Standards:
Favorites
(3)
Resources
(14)
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:
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)
Quadratic Functions Revisited, Day 2
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Students will rely on the structure of the quadratic equation, as well as dynamic graphical representations, to understand complex roots more deeply.
Standards:
Favorites
(1)
Resources
(12)
Review of Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
How is a complex number in standard form similar to a vector in unit vector form?
Standards:
Resources
(16)
Reflections
(1)
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)
Operations of Complex Numbers in Trigonometric Form
12th Grade Math »
Unit: Vectors and Complex Numbers
12th Grade Math »
Unit: Vectors and Complex Numbers
Big Idea:
Operations on complex numbers are easier when the complex number is in trigonometric form.
Standards:
Resources
(12)
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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