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Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students will know there is a complex number i such that i 2 = –1 and that every complex number has the form a+bi with a and b real. simplify expressions by add and subtracting and multiplying complex numbers (a + bi) by using algebraic properties. NCN.1 Learning intention: success criteria: 1. I will be able to use distributive property to complex numbers. 2. I will be able to combine like terms to simplify complex numbers. imaginary number a term that has an i. ex: Vocabulary Complex number the sum of a real number and an imaginary number. Has the general form a+bi. ex: a+bi (real part) (imaginary part)
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Page 1: Simplifying Complex numbers.notebook - Weebly€¦ · Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students

Simplifying Complex numbers.notebook February 05, 2018

Find the discriminant. State number of solutions and type.

Warm up

Students will • know there is a complex number i such that i 2 = –1 and that every complex number has the form a+bi with a and b real. • simplify expressions by add and subtracting and multiplying complex numbers (a + bi) by using algebraic properties.

N­CN.1Learning intention:

success criteria:1. I will be able to use distributive property to complex numbers.2. I will be able to combine like terms to simplify complex numbers.

imaginary number ­ a term that has an i.

ex:

Vocabulary

Complex number ­ the sum of a real number and an imaginary number. Has the general form a+bi.

ex:

a+bi(real part) (imaginary part)

Page 2: Simplifying Complex numbers.notebook - Weebly€¦ · Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students

Simplifying Complex numbers.notebook February 05, 2018

Example 1

steps Whya)

b)

Write as a multiple of i

• We can't have a negative number in a radical

√-1=i

• perfect squares come out of the square root

. Example 2

steps Whya)

b)

Write as a multiple of i

• We can't have a negative number in a radical

√-1=i

• perfect squares come out of the square root

.

Page 3: Simplifying Complex numbers.notebook - Weebly€¦ · Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students

Simplifying Complex numbers.notebook February 05, 2018

Simplify the following expressions.

a) b)

U­TRY11

Example 3steps Why

a)

b)

simplify

• replace i2 with -1

• i2=-1

• even powers give us positive answers

Example 4steps Whysimplify

c) d)• replace i2 with -1

• i2=-1

• odd powers give us negative answers

Challenge problem. Simplify i355 explain how you got your answer in a complete sentence.

remember to use academic vocabulary in your sentences.

pair share

Page 4: Simplifying Complex numbers.notebook - Weebly€¦ · Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students

Simplifying Complex numbers.notebook February 05, 2018

Simplify the following expressions.

a) b)

U­TRY13

Students will • simplify expressions by add and subtracting and multiplying complex numbers (a + bi) by using algebraic properties.

N­CN.1Learning intention:

success criteria:1. I will be able to use distributive property to complex numbers.2. I will be able to combine like terms to simplify complex numbers.

Example 5 steps Why

a)

b)

simplify • we can only add real numbers with real number and imaginary numbers with imaginary.

• we must distribute the negative before adding like terms

• combine like terms

• combine like terms

What if we add (4 + 2i) to problem (b)

What would be our new answer explain.

pair share

remember to use academic vocabulary in your sentences.

Page 5: Simplifying Complex numbers.notebook - Weebly€¦ · Simplifying Complex numbers.notebook February 05, 2018 Find the discriminant. State number of solutions and type. Warm up Students

Simplifying Complex numbers.notebook February 05, 2018

Example 5 steps Why

a)

b)

simplify • we can only add real numbers with real number and imaginary numbers with imaginary.

• we must distribute the negative before adding like terms

• combine like terms

• combine like terms

What if we add (4 + 2i) to problem (b)

What would be our new answer explain.

pair share

remember to use academic vocabulary in your sentences.

1. Add: (7 + 5i) + (8 ­ 3i)  2. Add: (2 + 3i) ­ (­8 ­ 6i) 

Example

Example

a) b)

find the productExample 7

steps Why

a)

b)

simplify• the square of a term is multiplying the terms by it self

• we can only add real numbers with real number and imaginary numbers with imaginary.

(associative property)

• i2=-1

Explain how the i infront of the parenthesis changes the last step on example (a)

remember to use academic vocabulary in your sentences.

pair share