Download CCSS.Math.Content.HSA.APRE.A.1

The Complex Number System
Name: ____TEACHER COPY ______ _______
CCSS.Math.Content.HSN.CN.C.7
Date: ______________________ Period: _____
Solve quadratic equations with real coefficients that have complex solutions.
Lesson Plan:
1. Hook:
Radical Sign: I love you! So why can't we be together?
Complex Number: It's complex.
2. Introduction and Vocabulary:
In order to understand and simplify complex numbers, we need to first discuss some vocabulary used with them: real
numbers, coefficients, radical sign, square root, commutative, associative, distributive, binomial, trinomial, factor,
imaginary numbers and complex numbers.
3. Guided Practice / Review:
After the vocabulary review, students simplify the following problems on their own:
A. i2
B. i7
C. i14
D. i17
Next, they plot the following complex numbers on the complex plane:
A. 2i
B. 3 + 2i
C. -1 + 2i
D. 3 - 2i
Simplify the following expressions.
A. (1 + 8i) + (2 – 3i)
B. (1 + 8i) - (2 – 3i)
C. (1 + 8i)(2 – 3i)
Check student work and review any discrepancies.
4. Independent Practice :
Students will review the quadratic formula and discriminants and apply them in problems that involve complex
number solutions. After reviewing as a group, have the students work independently on the specific examples.
At this point, I chose not to address the Fundamental Theorem of Algebra yet. If you choose to mention it here, see
lesson CCSS.Math.Content.HSN.CN.C.9 for suggestions. It's the fifth lesson down at
http://www.newmathteacher.net/algebra-2-lessons-complex-number-system.html.
Check student work and review any discrepancies.
5. Exit Slip:
Solve each equation. Include complex solutions.
1.
x2 + 9 = 0
2. 6x2 + 24 = 0
3. x2 + 64 = 0
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All Rights Reserved by NewMathTeacher.Net
The Complex Number System
Name: ____________________ ______ _______
CCSS.Math.Content.HSN.CN.C.7
Date: ______________________ Period: _____
Solve quadratic equations with real coefficients that have complex solutions.
Quadratic Formula
For an equation in the form:
Discriminant
Use the discriminant as a quick way to tell how many
and what type of solutions you will have:
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
Use the values of a, b, and c to solve for x:
−𝑏 ± √𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
Example:
The discriminant (D) is: D = b2 – 4ac
 If D > 0, then there are 2 real solutions
 If D = 0, then there is 1 real solutions
 If D < 0, then there are 2 complex solutions
Use the discriminant to test how many solutions the
equation to the left has:
3x2 + 5x - 2 = 0
D = b2 – 4ac =
a=
b=
c=
Solve each equation. Include complex solutions.
2. x2 + 18 = 0
2. 6x2 + 24 = 0
3. x2 + 49 = 0
4. x2 + 100 = 0
5. 3x2 + 108 = 0
6. x2 + 12 = 0
Be ready to explain to the class the key points of solving quadratic equations with complex solutions!
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net