complex arithmetic
DESCRIPTION
swdqdTRANSCRIPT
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Prepared by:Mr. Raymond B. Canlapan
COMPLEX ARITHMETIC
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1.4. Operations on Complex Numbers 1.4.1. Addition 1.4.2. Subtraction 1.4.3. Multiplication 1.4.3.1. Monomial: Distribution 1.4.3.2. Binomials 1.4.3.3. Special Products 1.4.3.3.1. Binomial Square 1.4.3.3.2. Conjugates 1.4.4. Division 1.4.4.1. Monomial Divisor
1.4.4.2. Binomial Divisor
SCOPE
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ADDITION
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(2x + 3y) + (x + 2y)(3x + 5y) + (2x + y)(3x + 3y) + (3x + 3y)
SET INDUCTION: REVIEW OF ADDING POLYNOMIALS
To add polynomials, simply combine like terms.
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Does the method of combining like terms in polynomials also applied in adding complex numbers?
What are the steps to be followed in adding complex numbers?
ESSENTIAL QUESTIONS:
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ADD:
¿5+8 𝑖
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HOW DO WE ADD COMPLEX NUMBERS?
1.
2.
3.
Add the real parts.
Add the imaginary parts.Express sum in standard form.
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)
ILLUSTRATIVE EXAMPLES: ADD THESE COMPLEX NUMBERS
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SUBTRACTION
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(6x + 7y) – (2x – 5y)
REVIEW: SUBTRACTING POLYNOMIALS
1.Change the sign of the subtrahend.2.Proceed to addition.
= 4x + 12y
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Does the procedure in subtracting polynomials applied in complex numbers?
ESSENTIAL QUESTIONS:
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FIND THE DIFFERENCE:
¿2+𝑖
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HOW DO WE SUBTRACT COMPLEX NUMBERS?
1.
2.
3.
Change the sign of the subtrahend.
Proceed to addition.
Express difference in standard form.
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)
ILLUSTRATIVE EXAMPLES: SUBTRACT
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SEATWORK: PERFORM THE INDICATED OPERATION
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MULTIPLICATION
A.Monomial FactorB.Binomial Factors
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3(2x + 5)2x(5 + 3x)7x(3x – 2y)(3x – 2) (5x + 3)(4x + 5) (3x – 7)
SET INDUCTION (QUIZ GAME): FIND THE PRODUCT (5 MINUTES)
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How do we multiply polynomials with a monomial factor?
How do we multiply polynomials with two binomial factors?
QUESTIONS:
Distribution Property
FOIL Method
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-> #1-10 -> # 11-20
A. MONOMIAL FACTOR
Using DPMA or DPMS
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-> # (21-30)# 31-40
B. BINOMIAL FACTORS
Using FOIL
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SPECIAL PRODUCTS
1. Binomial Square2. Conjugates
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C. BINOMIAL SQUARE
= 𝑥2+2𝑥𝑦+𝑦2
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C. BINOMIAL SQUARE
= 𝑎2+(2𝑎𝑏 )𝑖−𝑏2
Why?
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ILLUSTRATIVE EXAMPLES: FIND THE PRODUCT (TEAM-PAIR-SOLO)
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C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑥+𝑦 ) (𝑥−𝑦 )=¿ 𝑥2− 𝑦2
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C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑎+𝑏𝑖 ) (𝑎−𝑏𝑖 )=¿ ?
CONJUGATES
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complex numbers which differ only in the sign of their imaginary part
Find the conjugate of:
CONJUGATES
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ACTIVITY: PRODUCT OF CONJUGATES
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Tabulate the results:
ACTIVITY: PRODUCT OF CONJUGATES
Factors a b Product
2 3 25
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C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑎+𝑏𝑖 ) (𝑎−𝑏𝑖 )=¿ 𝑎2+𝑏2
Why?
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SEATWORK: FIND THE PRODUCT
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A. Monomial DivisorB. Binomial Divisor
DIVISION
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How do we divide complex numbers with monomial divisor?
How do we divide complex numbers with binomial divisor?
ESSENTIAL QUESTIONS
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How do we simplify
SET INDUCTION
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A. MONOMIAL DIVISOR
RATIONALIZATION
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reciprocal of reciprocal of
ILLUSTRATIVE EXAMPLES
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How do we make the denominator a rational number?
B. BINOMIAL DIVISOR
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B. BINOMIAL DIVISOR
CONJUGATION
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ILLUSTRATIVE EXAMPLES
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Reciprocal of
SEATWORK: SIMPLIFY THE FOLLOWING COMPLEX NUMBERS