4C.NCN.4.5.6.12.6.11
2011
Domain: Number and Quantity
Cluster: Represent complex numbers and their operations on the complex plane
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Standards: 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. 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°. 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.
Essential Questions
Enduring Understandings
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Why do we use
complex numbers?
What is the purpose of
using rectangular and
polar coordinates?
Why do we evaluate the
modulus and argument
of imaginary numbers?
Content Statements
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Students will represent
complex numbers on
the complex plane in
rectangular and polar
form.
Students will use
properties of addition,
subtraction,
multiplication, and
conjugation of complex

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Complex numbers are used
to model real world
phenomena as it relates to
electricity.
Complex numbers can be
used to generate interesting
patterns.
Distance between numbers in
the complex plane can be
calculated as the modulus of
the difference.
Activities, Investigation, and Student Experiences
1. Determine the length and midpoint (written as a complex
number) of each side of the triangle shown below.
http://wiki.warren.kyschools.us/groups/wcpscommoncorestanda
rds/wiki/e87bf/NCN6.html
4C.NCN.4.5.6.12.6.11

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numbers on the
complex plane to make
computations.
Students will calculate
the distance between
numbers in the complex
plane as the modulus of
the difference.
Students will calculate
the midpoint of a
segment as the average
of the numbers at its
endpoints.
Assessments
Students will solve problems similar to the below.
1. Represent graphically and give the polar form of 7 –
5j.
2011
2. http://education.ti.com/xchange/US/Mat
h/PrecalculusTrig/12675/Transitions_St
udent.pdf
(Activities on rectangular and polar coordinates)
4C.NCN.4.5.6.12.6.11
2. Represent 1 + j 3 graphically.
3. Find the modulus and argument of z = 4 + 3i.
2011
4C.NCN.4.5.6.12.6.11
The complex number z = 4 + 3i is shown in Figure 2. It has
been represented by the
point Q which has coordinates (4, 3). The modulus of z is the
length of the line OQ which we can
find using Pythagoras’ theorem.
(OQ)2 = 42 + 32 = 16 + 9 = 25
and hence OQ = 5.The complex number z = 4 + 3i.
Hence the modulus of z = 4 + 3i is 5. To find the argument we
must calculate the angle between
the x axis and the line segment OQ.
Website source:
http://www.mathcentre.ac.uk/resources/leaflets/sigma/complex_
numbers/sigma-complex9-2009-1.pdf
2011
4C.NCN.4.5.6.12.6.11
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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2011
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://www.purplemath.com/modules/comple
x3.htm
http://www.sparknotes.com/math/precalc/c
omplexnumbers/section4.rhtml
http://education.ti.com/xchange/US/Math/
PrecalculusTrig/12675/Transitions_Studen
t.pdf