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.

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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.

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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