Take two minutes to get your Notebooks, Signals, Calculators, & - PowerPoint PPT Presentation

AIM (3.1) : How do we identify and represent imaginary and complex numbers? Take two minutes to get your Notebooks, Signals, Calculators, & Student Orgzniers before we begin today's lesson. Alert! Alert!

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Alert! Do­Now Begins! Simplify each radical expression. Make sure your final answer has no negative terms in the radicand (underneath the radical sign). 3) 4) 2) 1)

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems 3) 4) 1) 2)

Announcements : A l e r t ! 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)

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems 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 Imaginary Number A number that is expressed in terms of the square root of a negative number (usually the square root of −1, represented by i ). The Imaginary Unit The imaginary unit, i , is the number whose square root is equal to negative 1.

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Simplifying Radicals with Negatives A radical is not considered simplified if there is a negative radicand. Ex. 1 Ex. 2 Ex. 4 Ex. 3

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Simplify each negative radical expression. Ex. 5 Ex. 6

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Simplify each negative radical expression. Ex. 5 Ex. 6 One Both Neither Correct Correct Correct

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems What do you notice about the answers when taking an even vs. an odd root of a negative number? Ex. 5 Ex. 6 Disuss with Your Neighbor

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Roots of Negative Numbers EVEN INDEXES: If the radicand is negative, the roots are imaginary only if the index is EVEN. ODD INDEXES: 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 Simplifying Square Roots with Negative Radicands Assess as You Work I got it! 1 2 I don't get it 3 I'm not sure

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

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Complex Number Any number that can be written in the form "a + b i " where a and b are real numbers. Ex. 3 + 2 i , ­4 + i , 5 ­ 2 i *All numbers can be written as a complex number. Ex. 7 i = 3 =

Aim 3.1: How do we identify and represent imaginary and complex numbers? HW: Worksheet 3.1, all EVEN problems Adding & Subtracting Complex Numbers Ex. 1 Ex. 2