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The modulus of E(+i)-* is equal to 328 (b) v82/16 248V62 /1612. The argument of (~1 + V3i) is equal to 27/3 2t/3 T/3 T/6 FT/6 57/6 ~5t/6...

Question

The modulus of E(+i)-* is equal to 328 (b) v82/16 248V62 /1612. The argument of (~1 + V3i) is equal to 27/3 2t/3 T/3 T/6 FT/6 57/6 ~5t/6

The modulus of E(+i)-* is equal to 328 (b) v82/16 248 V62 /16 12. The argument of (~1 + V3i) is equal to 27/3 2t/3 T/3 T/6 FT/6 57/6 ~5t/6



Answers

Decide whether each of these integers is congruent to 5 modulo $17 .$
$\begin{array}{ll}{\text { a) } 80} & {\text { b) } 103} \\ {\text { c) }-29} & {\text { d) }-122}\end{array}$

So we want to find a dip and mods for various questions. So first we have a is equal to 2 to 8 and is it 119? So the way I will do this one is a bit different from how it used to be normal. It's officially Let's find it. Do you? So a do em easy going to just one floor 80 by my So if you do a divided by in this case, get 1.915 So the floor that is this one No, a mud in is doing speed. A modest by M tons by the floor a m So in this case, this is true to eight miles by M, which is just one a month. A divided by AM is just once em is 119 So this just gives you 100 and one eye Be. We have nine years there nine and 2 to 3. So a do you m is going to be the floor off nine years there nine by about 2 to 3. So this is for this is for you went 39 and flows. This is 40 So a more m is going to be 90 desert ninth. Subtract 40 um, tires y 2 to 3. So this should give you a mine for see, we have negative. 10101 and 333 So a do em, which is eager to full 80 Bye bye m, which is just full of native 1010 or one through over 333 So this is the floor off negative. 30.33 That since this is a negative number, this is actually negative. 31 said a more em. We did the same thing. So that's just going to be a 10101 We have minus by the floor office. So which is negative? One attracting almost applied by M so multiplied by 333 So this is fun to be negative. 101012 Negatives become Plus, don't you want to tell the 333 which would give you ju to to and we have d negative. 765432 and 38271 So once again, eh? Do you have Mm. Is this going to be Nick or the floor off negative. 765432 over 38271 So this is negative to zero point joy 003 So this is just negative. 21 and the full A certain mother is going to be negative. 765432 Subtracting monitoring. One multiplied by the M Sandwiches 38271 which is negative. 765432 Just 21 ton by 38271 was just 38259

Okay, So this question we want to compute various on various numbers. I guess so. Three Rio too more by So to compute this, we use so much little syrup. So by famous little serum three to the four is equivalent to one month flight. So we have 3302 is equivalent to 3 to 4 times less 70 by plus fire to this is quote money. Why, This is just going to be, um, reserve board. Traversoni by has a three squared more five. And this becomes one said this is just three swift. So nine more five, which is just four months by now. 3302 What's seven? We did the same thing by Fermat's little serum. We have three sixes gripping to one most seven now three to the 302 is equivalent to three to the 50 times last six suss fight too. So then this is almost seven. So then this is equivalent to three to the 50 tons of six times by three square marks. Seven becomes one bite for a single theory. So this is just nice. Boys in line, Mom seven. This is just too months. So now for the last one, we have three to the 30 shoot. Uh, what? Seven. So, by Thurman, it's little theory. We have 3 to 10 is equivalent to one. Well, you let me so rewarding this. We can rewrite this as, uh, three to the three times by 10 suspects, 100. But say times 10 that's what to it's equipment, too. Read, uh, 10 time by 30. That's what you tied by three squared Mark Levin. This becomes one. So this is this mine say is equivalent to nine monkey. Now, what will use, though, is for 300 truth in what five will use that this is equal to Meyer for 302 months. Seven. We use that this is equal to nine. And for 302 more 11. We used it to keep it in mind. So in summary, then what we have is 3302 is equivalent to nine. Well, why three to the 302 is equivalent to nine. Well, seven and three to the 302 is equivalent to nine model. So by the Chinese remainder theorem, what we have is three to the 302 is equivalent to nine more by seven times, so this is just fine more 300 and 85.

I want to find the engages. Which are pretty good at this my normal expression. But that led us and lives here. Um. The animal expansion for one plus one or an be here. All of the peoples variable expression here we have this one plus one over. Can call him the barbie have 10,000 key here. It is one plus one over. N. To the power end with the unless those here one plus one hour. End to the far end Expanded. Where does one class? And do you want one or n. plus permission being a cake was too to N. N. C. K. And we have one over. And the barkeep. Now we just right this here so we get to death. It will be too true. Last permission cake was true Joanne and we have one over. Okay Factorial that we go from here and Tiki and then we get and a -1. And so until and negative people as well. Because when you explained it we get and sectoral over a negative K. Pictorial. So that is going to log and we get still a negative plus one or where we have entered the market. Well let's be endorsed ted now to see you its numerator last than the denominator metamaterials 10 times 10 times 10 and so on. Still gay dumps we have. So the numerator is less than denominator. So therefore so you can write this as That's less than equal to 2-plus formation equal to two True and one over. Okay. Victory. Because this fraction here is less than or equal to what to take a K. Equal to want then it's coming out to me we have and or end and that gives it is You have to be one and I would just look at here this park throat Stephen addict. True plus the mission capable to to end one over K. Times negative one get negative too and so on. But this is less than it will do. We have two plus commission equal to To end one over. Okay. Do you think you want? Why is this because they we have nominator, bigger diameter is smaller. This part is coming out to be bigger here so this part is smaller so you're less than equal to plus the mentioned cable to to end one over. T. Can everyone they will take care of. So for you have taken here K. Equal to it's turning out to be equal so it's gonna be given like this. Now if you just saw this it is given us equal to Plaster Mission Equals two To end 1/-1 negative one over keep Have given us two plus so it will become now 1/1 negative 1/2. Last one over to 91 of the trees. So the cancellation will be there till we get negative one over end. So we get here two plus one negative one over end. Well B three negative one or so. Now this is coming up to me 3 -1 over n. So we get for angrier than equal to one. We have this part coming out we let someone over to 1/3 so we get it out Less than three. So we have got there marriage the my normal series here one plus one over 10,000. About 10,000. It's coming up to be Less than three. The indigenous greater than that So that you can ask three or why? Thanks and seven So the answer is coming up to be in the auction. We have trees right orders right. Five is right and seventies right thanks.

Okay, so this fishing want to keep you Paris Months surfaced in happy is far to the 2000 and three more seven. So what we do know what? So you want to write this in terms of 6 10% number, so have 2000 and three is equal to 334 times six months. So we can write. This number is being fired. Six All this to the 334 multiplied by five minus one. Mom. So bye. Fermat's last year. You know that this number is one. So 12 334 students and one to this number. You just left this five in verse. What? Seven. You know, we know that five investors just equal to three months. Seven. So our next one is Bob's, the 2003 more 11 I wanna live in. So once again, we want to do the same thing, but in terms of 10th. So we know that 2000 and breezy to 200 times by 10 plus three. So you can write This number is being far too 10 that she 100 times five here more 11. This now becomes one So this is five. Q five is just one of five more 11 side. This is just for 11. Well, you know, and our last 112 2003 More 13. But the same thing with 12. So we have 2000 really easy with you. 167 times by whoa. Modest one. So then we can write this number. She as being boxed the 2000. Think about it. What's 12 to 1 67 as a five minus one more 30. A famous last serum. This becomes one sense is why invest Mole 13. And this is just eight more busy now for the next pot. One of these charms remain in theory, into flying by to the 2003 more 1000 and one. So we know that one doesn't have one is equal to seven times by 11 times. So I really need to do Is this soul on what we have from here? Pay this question that fight to the 2000 and three. If I just let this be eggs, we know that X more. Most seven gives you three x more 11 days. You four and x modern more 13 gives you a So this is China's remaining serum to solve this? No. So how did this? So we really to find seven times, like 11 times, like 13. So this is 1001. Um, they need 1000 and one divided by seven. So this is just 143 3 1001 divided by 11 is just money one and 100. 1001 Divided by 13 with the 77. Now, we need to find 143. Inverse, most seven. It just is a calculated for this. Just five. My one ingress more. 11. This is just four. And I'm 77. Inverse mold. 13. This just thinking, Paul. So now about Hein so much. I never made it there. The answer. Just be three times 100 43 5 plus four has anyone for plus 877 So we write that three times. 143.5 plus four times by 91 tenant only one time full plus eight times for 77 times talk. I'm just gives you 10,000. Monitor. Miami Three more One. There is one which is just equipment to know. 900 and a three. Mole 1000 and one


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