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AIM (3.1) : How do we identify and represent imaginary and complex numbers?

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Do­Now Begins!

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

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1) 2) 3) 4)

Simplify each radical expression. Make sure your final answer has no negative terms in the radicand (underneath the radical sign).

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

1) 2) 3) 4)

Announcements: 1) (Optional) DeltaMath assignment: Review #3, due Friday.

(Every 10 questions complete = +2 on Midterm Exam.)

2) Tutoring: Mr. Lo is available after school Monday & Friday: Right after school 3) MACS Robotics club does not meet this Wednesday (Halloween)

A l e r t !

What are Imaginary Numbers for?

Used for: Signal Processing (Cellphone signals), Electricity (AC & DC Waves), Quadratics (when parabolas don't touch the x­axis)

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

A number that is expressed in terms of the square root of a negative number (usually the square root of −1, represented by i ).

Imaginary Number

The imaginary unit, i , is the number whose square root is equal to negative 1.

The Imaginary Unit

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Simplifying Radicals with Negatives

• Ex. 1
• Ex. 2
• Ex. 3
• Ex. 4

A radical is not considered simplified if there is a negative radicand.

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

• Ex. 5
• Ex. 6

Simplify each negative radical expression.

• Ex. 5
• Ex. 6

Simplify each negative radical expression.

Neither Correct Both Correct One Correct

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Disuss with Your Neighbor

• Ex. 5
• Ex. 6

What do you notice about the answers when taking an even vs. an odd root of a negative number?

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

EVEN INDEXES: If the radicand is negative, the roots are imaginary only if the index is EVEN. ODD INDEXES:

Roots of Negative Numbers

If the radicand is negative, the roots are real and negative.

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

What is the imaginary unit and when do we use it to simplify expressions?

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Simplifying Square Roots with Negative Radicands

Assess as You Work

1 3

I got it! I don't get it I'm not sure

2

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems 0 ­ 3 Correct 7 ­ 8 Correct 4 ­ 6 Correct

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems

Any number that can be written in the form "a + bi " where a and b are real numbers.

Complex Number

• Ex. 3 + 2i, ­4 + i, 5 ­ 2i

*All numbers can be written as a complex number.

• Ex. 7i =

3 =

Adding & Subtracting Complex Numbers

• Ex. 1
• Ex. 2

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems