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Algebra 2
Complex Numbers
Lesson 4-8 Part 2
Goals
Goal
• To find complex number
solutions of quadratic
equations..
Rubric
Level 1 – Know the goals.
Level 2 – Fully understand the
goals.
Level 3 – Use the goals to
solve simple problems.
Level 4 – Use the goals to
solve more advanced problems.
Level 5 – Adapts and applies
the goals to different and more
complex problems.
Vocabulary
• None
Essential Question
Big Idea: Solving Equations
•
How are complex numbers related to the
solutions of quadratic equations?
Complex Solutions
If a quadratic equation with real coefficients has nonreal
solutions, those solutions are complex conjugates.
Complex solutions always occur in pairs, complex
conjugate pairs.
Helpful Hint
When given one complex solution, you can
always find the other by finding its conjugate.
Example:
Solve the equation.
Take square roots.
Express in terms of i.
Example:
Solve the equation.
5x2 + 90 = 0
Add –90 to both sides.
Divide both sides by 5.
Take square roots.
Express in terms of i.
Your Turn:
Solve the equation.
x2 = –36
Take square roots.
Express in terms of i.
Your Turn:
Solve the equation.
x2 + 48 = 0
x2 = –48
Add –48 to both sides.
Take square roots.
Express in terms of i.
Your turn:
Solve the equation.
9x2 + 25 = 0
9x2 = –25
Add –25 to both sides.
Divide both sides by 9.
Take square roots.
Express in terms of i.
Example:
Find the zeros of f(x) = 4x2 + 3x + 2 using the Quadratic Formula.
f(x)= 4x2 + 3x + 2
Set f(x) = 0.
Write the Quadratic Formula.
Substitute 4 for a, 3 for b, and 2 for c.
Simplify.
Write in terms of i.
Your Turn:
Find the zeros of g(x) = 3x2 – x + 8 using the Quadratic Formula.
Set f(x) = 0
Write the Quadratic Formula.
Substitute 3 for a, –1 for b, and 8 for
c.
Simplify.
Write in terms of i.
Your Turn:
Find the zeros of each function by using the Quadratic
Formula.
1. f(x) = 3x2 – 6x – 5
2. g(x) = 2x2 – 6x + 5
Essential Question
Big Idea: Solving Equations
•
•
How are complex numbers related to the
solutions of quadratic equations?
Every quadratic equation has complex solutions.
Sometimes, these complex numbers only have
real parts. When a quadratic equation has no real
solutions, use square roots or the quadratic
formula to find the imaginary solutions.
Assignments
• Section 4-8 Part 2, Pg 275 – 277; #1 – 4 all,
6 – 14 even, 24, 30 – 44 even.