Complex arithmetic
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Transcript of Complex arithmetic
Prepared by:Mr. Raymond B. Canlapan
COMPLEX ARITHMETIC
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
ADDITION
(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.
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:
ADD:
¿5+8 𝑖
HOW DO WE ADD COMPLEX NUMBERS?
1.
2.
3.
Add the real parts.
Add the imaginary parts.Express sum in standard form.
)
ILLUSTRATIVE EXAMPLES: ADD THESE COMPLEX NUMBERS
SUBTRACTION
(6x + 7y) – (2x – 5y)
REVIEW: SUBTRACTING POLYNOMIALS
1.Change the sign of the subtrahend.2.Proceed to addition.
= 4x + 12y
Does the procedure in subtracting polynomials applied in complex numbers?
ESSENTIAL QUESTIONS:
FIND THE DIFFERENCE:
¿2+𝑖
HOW DO WE SUBTRACT COMPLEX NUMBERS?
1.
2.
3.
Change the sign of the subtrahend.
Proceed to addition.
Express difference in standard form.
)
ILLUSTRATIVE EXAMPLES: SUBTRACT
SEATWORK: PERFORM THE INDICATED OPERATION
MULTIPLICATION
A.Monomial FactorB.Binomial Factors
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)
How do we multiply polynomials with a monomial factor?
How do we multiply polynomials with two binomial factors?
QUESTIONS:
Distribution Property
FOIL Method
-> #1-10 -> # 11-20
A. MONOMIAL FACTOR
Using DPMA or DPMS
-> # (21-30)# 31-40
B. BINOMIAL FACTORS
Using FOIL
SPECIAL PRODUCTS
1. Binomial Square2. Conjugates
C. BINOMIAL SQUARE
= 𝑥2+2𝑥𝑦+𝑦2
C. BINOMIAL SQUARE
= 𝑎2+(2𝑎𝑏 )𝑖−𝑏2
Why?
ILLUSTRATIVE EXAMPLES: FIND THE PRODUCT (TEAM-PAIR-SOLO)
C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑥+𝑦 ) (𝑥−𝑦 )=¿ 𝑥2− 𝑦2
C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑎+𝑏𝑖 ) (𝑎−𝑏𝑖 )=¿ ?
CONJUGATES
complex numbers which differ only in the sign of their imaginary part
Find the conjugate of:
CONJUGATES
ACTIVITY: PRODUCT OF CONJUGATES
Tabulate the results:
ACTIVITY: PRODUCT OF CONJUGATES
Factors a b Product
2 3 25
C. SPECIAL PRODUCT OF THE SUM AND DIFFERENCE OF TWO LIKE
TERMS
(𝑎+𝑏𝑖 ) (𝑎−𝑏𝑖 )=¿ 𝑎2+𝑏2
Why?
SEATWORK: FIND THE PRODUCT
A. Monomial DivisorB. Binomial Divisor
DIVISION
How do we divide complex numbers with monomial divisor?
How do we divide complex numbers with binomial divisor?
ESSENTIAL QUESTIONS
How do we simplify
SET INDUCTION
A. MONOMIAL DIVISOR
RATIONALIZATION
reciprocal of reciprocal of
ILLUSTRATIVE EXAMPLES
How do we make the denominator a rational number?
B. BINOMIAL DIVISOR
B. BINOMIAL DIVISOR
CONJUGATION
ILLUSTRATIVE EXAMPLES
Reciprocal of
SEATWORK: SIMPLIFY THE FOLLOWING COMPLEX NUMBERS