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Can Based 1 have? 1 the 1 degree of the polynomlal 2 f(z) ven below 6) ( { what is the maxlmum 15) number { 1...

Question

Can Based 1 have? 1 the 1 degree of the polynomlal 2 f(z) ven below 6) ( { what is the maxlmum 15) number { 1

can Based 1 have? 1 the 1 degree of the polynomlal 2 f(z) ven below 6) ( { what is the maxlmum 15) number { 1



Answers

If degree of both $f(x)$ and $[f(x)+g(x)]$ is 18 , then degree of $g(x)$ can be (1) 18 (2) 9 (3) 6 (4) any one of these

In question. We have a complex numbers his record so one plus, uh, one minus three. About six. It is the Notaro complex number. Be physical one minus three. Now the value off for this convicted in in former are cost adapters. I scientific Uh, yes, I am So can be found on using this one script. That's little squid Artis who turned before it is too. No, the world will be has posted a positive sign 90 days minus. So the blue plan today is negative which is possible only in second and fourth quarter since scientist eyes negative and positives positives that Twitter must be lying in the fourth quarter. And there you guys 300 years now using the move it We have a physical with people six So for reds and run complex number our course it up the site in pewter If it is raised to the power and people in becomes our power in Paraguay cause into topless I signed in So the power to which it is Ray's regiment declare with the angles people are six becomes to power six course six Indo he dies 380 Yes, I saying in six in 300 degrees is in place. Uh, people six physical, 64 more prepared, cause 1800 less by saying 1800 1800. So simplifying this, putting the willies off for cause 1800 signing again. Birth. You get 61. We hear the valley off sign 18 under t zero and cause 18 under his one. So 64 is the final badly off people. Six. The value off complex number is 64.

For this question. We have another tomorrow steering problem or we have one minus Route three. I all raised to the sixth power. So in order to do this, we need to put this cup this complex number in trig form. So let's draw or plot this point on the complex plane. So we have our rials and imagine Aires are really component is one. And our imaginary component is Route three or negative Route three. So that will be about here. So we have this 0.1 minus root three I and this distance this length will be our and this angle is data. So let's draw this triangle a little bigger. So we have our right triangle with this angle, Fada. And then this side is one and this side is negative. Route three. So like many of our previous problems, we've had to look out for special right triangles and this problem is no exception. So if this side is X, we have this side is X ray three again. The negative sign is not the length that just tells us the direction. So because we have X and X ray three, this tells us this is a 30 60 90 right triangle. So this angle theta is going to be 60 degrees, but we're below the access. So we're gonna call this negative high over three negative 60 degrees and ah, it follows then that this side, the high pot news, is going to be two X and since X is one, the side will just be too. So now we have the complex. We have the trick form. So we have to sis Negative pi over three, all raised to the sixth power. So now with our the're, um thus tells us that or says they, uh, raised to the and power is our to the end says, and they'd, uh So for this problem, we have to to the six sis six times negative pi over three. So now when we simplify to to the sixth is going to be 64. Then we have cysts and then six times negative pi Over three, we have six divided by three. So this simplifies to negative two pi, so that will be in negative too high, which is the same thing as zero. But we're gonna leave as negative two pi for now. So we can leave our answer like this, or we can simplify it one step further. So because the full form of this is 64 times co sign of negative two pi plus I, I'll put this in parentheses. Plus I sign of negative two pi. Well, sign of two pi or sign of zero is going to be zero. So all of this cancels out and co sign of zero is one. So all of this is just one. So then we have 64 times one, which is obviously going to be 64. So 64 will be our answer for one minus root three I raised to the six power. This equals 64. So there we go. That is our answer.

We want to upload this complex number and also converted into polar form. If you compare it with a plus, I oughta be 1/4 to minus one and be quarto minus one. So we deplore this complex numbers that's ever that report One comma, minus one in rectangular coordinates system. So we will move on unit to the left and one unit down. So disease complex number jet, and we will join it with or reason. And the polar form will be given s Zedd. Equal toe are coast to topless iota signed. Tita, there are is called a mortal s and P ties argument and for complex number do that will be angle mitt by complex number with the re Alexis. So this is your top. So they lay off our is given by square. Root off is scare plus be scared. We'll put the value off a nb so scared off. Minus one scared plus minus once get equal to scare it off toe. And for a look to travel lose 10 to taik will to be divided by a We'll put the value of being a It is one and we can see that dying complex number. Region tired of quarter. So angle will be We know that 10 5 i forties one but complex numbers in third Cordant So Tita will be by plus bye bye for dirties Fight by way full. So you will put the value off are NT time Polar form So poor form off minus one minus. I were tackle big units that equal to wrote to course fight by by four unless iota sign fight by way four.

In this question were given to complex numbers in better form. Has he won this three cents by over 400 Louis five sets by over six. And we have to calculate their products and the format to do so. I wrote here on the right. We multiply there, ma July and we asked the angles. So in our case are one times are too is three times five. This is 15 and we have to add their angles. So he goes to the 1% by over four Bush like over six. Then to add freshens, we have to ah, write them in different forms or not. The shame denominator. Um, we can usually denominator 12. So now we got you're gonna write by over four a street by number 12 and by over six s, Dubai over 12. And then we find that this there some it's five by. And so using this we see that product. The one thanks is 15. The product will start much lie on, insists the sum of their angles, which is five bye number 12


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