Welcome to Clip from Spiral logo

Interactive video lesson plan for: Operations on Complex Numbers Product Quotient Power Root Polar Rectangular

Activity overview:

Playlist: https://www.youtube.com/playlist?list=PL3Gnjw2fQSnE6P7bLxwz5PbGixT5dbrrB

in polar form are going to start off by taking a look at some of the formulas that we're going to be using him for the process. So let's write it down formulas for the letters right so let's start with of the product formula down it, but the formulas basically apply to the following situation unless a of for complex numbers to the one the one S R one does the radius times cosine data, oneI sign Theta one and another complex numbers the two bridges are to cosine Theta to plus I sign Theta to we have the following formula. So for product. The product of expressed as the one times elite to is given by of our one are to find cosine Theta one plus Theta to plus five sign Theta one was stated to write so let's take a look at is, for second one is the formula tallest to do well to multiply and to complex numbers in polar form, so is that will simply just multiply the radii and add the animals okay so that's how you find product of on complex numbers in polar form. Right let's take a look at the next formula which is for the quotient for the quotient the one over the two please keep track of the order here is equal to our one over our to times you see in this in the case of the product that was times now is a quotient cosine that can you guess what we done with the angles here this was a product became a quotient this is the Psalm to be the opposite which is a different so Theta one minus stated to plus I sign beta one minus negative attack in a we also have a formula for the power hours you to repeated multiplication so if we have is the one to the and power what you going to have is that our one multiplied by itself in number of times repeated multiplication can be expressed using exponents so that will be our one to the and power times cosine and we multiply zero let's of and times are good at one to itself and times to repeated addition is multiplication to get have an Theta one plus the same story with the sign angle this agreement enter the one also and then we also have the root formula the the answer to of is the one which is equal to the one race to the one of her and is an effort property of exponents this can the written as our one race to the one over and the length root of our one times cosine Theta one over and plus I sign Theta one over and okay this is the formula for finding the principal roots principle roots the other roots, but Tom this one is used to find the principal right of with all these formulas a minus is go ahead and consider the first example of example 1 of four is the one equals three of cosine pirate three plus I sign private three and on we have another complex number of equal forms the two which equals five cosine pirate six plus I sign pirate six that now this situation is going to find the following a were going to find the one times E2 to find the one times E2 we also going to find the two over is the one and undefined for the part C with six is that again look for the one race to the third power and name for the flask welcome part D then assigned of the fourth root of the two okay so these are the of F finding example one is that with the first one so for part a we looking for is the one times E2 so remember the process of we're to for product or to multiply the radii and add the angles okay so this is our one in this is our to sustain one this is stated to let me just indicated for you see can see this is of our one are one basically means to radius of the first complex numbers in polar form and an Theta one is the radius of the angle of the first of complex number polar form so the same idea places the the second complex number are to Theta to write now we can go ahead and of compute the product stated one also one thing one and is about complex numbers in polar form is that these two angular arguments are always to say right so the one the two we going to have three times five that's our one times are to cosine the one plus Theta to is pirate three plus pie over six plus five sign private three plus five or six okay so is pilot three plus power six is our scratch work over here pirate three plus pirate six and to find LCD the multiply by two top and bottom we have to pie over six plus pirate six that's of three pirate six which reduces to pie over to okay so that's the of angular value of the some of these two angles the one plus stated to so our final result is going to be of three times five fifteen fifteen cosine pi over two plus I sign pie over to okay so this is your answer in of polar form so is indicate the form you can write this erectile a form. Also but this is is the answer in polar over for okay let's take a look at question number the be part one of find the one answer is E2 divided by see one now for consult the quotient formula you

Tagged under: law sines,law cosines,vectors,plane,dot,complex numbers,magnitude,direction,geometrically,operations,oblique,AAS,ASA,SSA,ambiguous,component,real,demoivre,+bi,imaginary axis,rcos θ,isin θ,argument,modulus,polar,restricted,quadrant,multiplication,division,powers,root,nth root,theorem θ + sin θ,scalar,cross product,larson,examples,steps, ,python,applications,basics,book,notes,cheat sheet,desmos,equations,arctan

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Operations on Complex Numbers Product Quotient Power Root Polar Rectangular on Google+ Share Operations on Complex Numbers Product Quotient Power Root Polar Rectangular on Twitter Share Operations on Complex Numbers Product Quotient Power Root Polar Rectangular on Facebook Pin Operations on Complex Numbers Product Quotient Power Root Polar Rectangular Email Operations on Complex Numbers Product Quotient Power Root Polar Rectangular

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome