Download 4C.NCN.3.12.6.11

4C.NCN.3.1.12.6.11
2011
Domain: Number and Quantity
Cluster: Perform arithmetic operations with complex numbers.
Standards: 3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Essential Questions
Enduring Understandings
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How do you use
conjugates?
What is the relationship
between conjugates and
real numbers?
What are real-life
situations involving
complex conjugates?
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Content Statements
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Students will find the
conjugate of a
complex number.
Students will use
conjugates to find
moduli.
Students will use
conjugates to find
quotients of complex
numbers.
Assessments
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Complex conjugates are
number pairs of the form a +
bi and a – bi.
Modulus of a complex
number is the distance of the
number from the origin.
To find the modulus of a
complex number, take the
square root of the product of
the complex number and its
conjugate.
Quotients can be expressed
as a fraction. Multiply the
numerator and denominator
by the complex conjugate of
the denominator to obtain a
real number in a
denominator.
Activities, Investigation, and Student Experiences
1. Activity: Using NSpire calculators to find quotients of
complex numbers.
http://education.ti.com/calculators/timathnspired/US/Act
ivities/Detail?sa=1010&t=1179&id=10888
2. http://mathforum.org/mathtools/activity.html?id=818&
From the Math Forum-A children's book-on-the-Web
from Australia, designed to introduce complex numbers
in story form in a way that is intuitive and enjoyable for
students.
3. Evaluate the expression and write the result in the form a
+ bi.
(2  3i)(5i)
2  3i

4C.NCN.3.1.12.6.11

2011
Students will answer short-answer questions, showing
all work. For example:
1. Evaluate the expression
2i
and write the result in the
4  3i
form a + bi.
1 4

2. Evaluate the expression
and write the results in
1 1
the form a + bi.
3. Use the complexconjugate to determine the modulus.
3
1
i
3
Equipment Needed:
Teacher Resources:
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Smart board
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Calculators (graphing)
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White boards
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Overheads
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http://www.purplemath.com/modules/comple
x2.htm
http://www.khanacademy.org/video/complex
-numbers--part-2?playlist=Algebra
http://www.khanacademy.org/video/complex
-numbers--part-1?playlist=Algebra
http://www.mathworksheetsgo.com/algebracalculators/complex-numbercalculator.php
http://education.ti.com/calculators/timathnspired/US/Activiti
es/Detail?sa=1010&t=1179&id=10888
http://mathforum.org/mathtools/activity.html?id=818&