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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.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)

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

.

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

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.

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