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Transcript
Complex Numbers and
Solving Equations
Honors Algebra II with Trig.
Ms. Lee
Essential Stuff
Essential Question
• How do you simplify expressions
involving complex numbers?
Essential Vocabulary
• Imaginary Number
• Complex Number
• Complex Conjugate
Imaginary Numbers
• Not all quadratic equations have
real number solutions, so to
overcome this problem,
mathematicians created an
expanded system of numbers
using the imaginary unit 𝐢
Imaginary Unit, 𝒊
𝒊=
−𝟏
𝟐
𝒊 = −𝟏
• These properties allow us
to simply the square root of
a negative number.
Complex Numbers
• A complex number is a number that
contains a real and an imaginary part.
• The standard form:
Real
𝒂 + 𝒃𝒊
Imaginary
Add/Subtract/Multiply
Add and Subtract
1.
2.
Combine Like Terms
Write in Standard Form
Multiply
1.
2.
3.
FOIL
Replace 𝒊𝟐 with −𝟏
Combine Like Terms/Standard Form
Dividing with Complex Numbers
Divide
• Multiply the numerator and
denominator by the complex conjugate
• Complex conjugates are two complex
numbers of the form:
𝒂 + 𝒃𝒊 and 𝒂 − 𝒃𝒊
Complex Conjugates
The product of complex
conjugates will always be
a real number.
Homework
• Homework 5.6: Complex Numbers
Homework:
• Page 35 Problems 4, 6, 8, 14
• Pages 45-48 Problems 16 – 32 even,
51, 53, 54, 56, 74