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
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