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数学 大学生・専門学校生・社会人

複素数の問題です。 全て解いてほしいです。 特に問題4の解説をよろしくお願いします。

問 ■複素平面と極形式 題 複素数zは:=Rez+ i Imz と書くことができ、実部 Re z をx座標、虚部 Im:をy座標に見立てることで、 ガ ウ こを2次元平面上の1点として捉えることができる。この平面を複素(数)平面ないしGauss 平面と呼ぶ。 一方、ある複素数zを、二つの実数r,e(ただしr>0に制限す る)を用いて Im ミ=ree という形で表わしたものを:の極形式表示と呼ぶ。e の逆数は -1 Im:=rin 1 で定義する。 er Imz 問[]()r= |, tan @ = が成り立つことをそれぞれ示せ。 Rez (i) 逆数の定義に基づいて (e")= e-t0 であることを示せ。 Re Rez=r このようにこの絶対値であるrは複素平面における原点(0+ 0i) から、までの距離を表わし、0は原点とこを結ぶ線分が実軸となす 角を表わす。はarg z とも書き、偏角 (argument)(物理や工学で はしばしば位相(phase))と呼ぶ。原点の周りを一周しても同じ点 に戻ってくることから、0には 2x ラジアン= 360度の整数倍の不 定性がある。また、0+0iの偏角は定義されない。 図1 複素平面。 偏角と加法定理 絶対値が1の二つの複素数 Im 21= COs # +isin @, 2= cos #,+i sin @。 を考える。ここで0,,02 は実数とする。 問 [2]() 積22 を計算し、三角関数の加法定理とオイラーの公 式を用いて極形式表示に直せ。また、同様にして商z/zz = zi の極形式表示も求めよ。(i) 21,22の複素平面における表示を図2 とする。このとき、積」みと商z/を複素平面に図示せよ。 0.5 Re -10 -0.5 0.5 21= e,22= e であったから、小間 (i) のとくに積の方の結 果から、次の基本的な指数法則が成り立つことが理解できる: 基本的な指数法則 -0.5 実数,に対してelh el = e(h+h)が成り立つ。 図2 と2の複素平面における表示。 また、小間(i) の結果から、22= e' hを掛けることで」から偏 角がだけ反時計回り方向に回り(角度が+)、2で割ることで 2」から偏角はだけ時計回り方向に回る(-)ことが納得できる。

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英語 高校生

見辛かったらすみませんが、問2の英作文の添削をしていただきたいです🤲

2015年度 英語 13 They should not have to lose their livelihoods. Secondlv. although I agree 次の英文は、英語のディベートの授業での対話です。この対話を読み,下の問い に答えなさい。 with Keiko that climate change is a serious problem, I think air travel is a much less damaging source of carbon pollution than, for example, burnimg MR. ROBERTS: Good morning, everybody. Today we have the first of our Coal. We should address these more serious causes first. Finally, the most student debates. The topic this morning is air travel, and the argument is. 法 important reason is the issue of freedom. People in a democracy expect the “Domestic air travel in Japan should be discouraged." Keiko will first argue right to travel as they wish. It has made our lives more convenient and in favor of the proposal and Junko will speak against. Over to you, Keiko. created more opportunities for everyone. We should not reduce our quality of life. Thank you for listening. KEIKO: Good morning, everybody. I am going to speak today in favor of the proposal. Limitless air travel inside Japan is a luxury that we can no longer MR. ROBERTS: Thank you to our two speakers. Now, are there any afford. The main reason is that it is extremely damaging to the questions from the audience? environment. The carbon gases produced by aircraft are very high and are a 頭人 proven cause of global warming. Therefore, we should try and reduce air 問1 次の(1)~(5)の文について, 本文の内容と一致するものには○.一致しないも travel as much as possible to protect the environment, not only for Japan but のには×を,それぞれ解答欄に記入しなさい。 also for the whole world. Secondly, air travel is actually unnecessary within the four islands of Japan. Now, while I appreciate that travel to Okinawa is (1) Keiko's main reason for opposing domestic air travel is the damage it a different case, there are efficient train services throughout Japan that are causes to the environment. h fast and environmentally friendly. These make an excellent alternative to air (2) Keiko thinks that air travel is cheap and efficient. flights, so there is really no need to use airplanes in most cases. Finally, (3) Keiko recommends that people travel between Okinawa and mainland there is an economic reason. Air travel is expensive for passengers because Japan by ship. the price of fuel keeps increasing, but airline companies are still struggling (4) Junko thinks that climate change is not an important problem. to make profits. Moreover, regional airports often cannot attract enough (5) Junko thinks that a lot of jobs will be lost if air travel is reduced. customers, and, overall, the industry is not cost-effective, It's time to admit that air travel is too damaging and expensive to be sustainable. Thank you. 問2 次の質問に英語で答えなさい。 Which of the two speakers do you more agree with? Give at least one JUNKO: Thank you, Keiko. I am going to disagree with the proposal for three reason for your answer. (解答欄:13.8cm×4行) reasons. Firstly, I think there is a strong economic case to support flying. Many jobs depend on air travel, not just the pilots and cabin staff, but also people who work in airports or for airlines, or who rely on fast transport.

回答募集中 回答数: 0
英語 高校生

見辛かったらすみませんが、問2の英作文の添削をしていただきたいです🤲

2015年度 英語 13 They should not have to lose their livelihoods. Secondlv. although I agree 次の英文は、英語のディベートの授業での対話です。この対話を読み,下の問い に答えなさい。 with Keiko that climate change is a serious problem, I think air travel is a much less damaging source of carbon pollution than, for example, burnimg MR. ROBERTS: Good morning, everybody. Today we have the first of our Coal. We should address these more serious causes first. Finally, the most student debates. The topic this morning is air travel, and the argument is. 法 important reason is the issue of freedom. People in a democracy expect the “Domestic air travel in Japan should be discouraged." Keiko will first argue right to travel as they wish. It has made our lives more convenient and in favor of the proposal and Junko will speak against. Over to you, Keiko. created more opportunities for everyone. We should not reduce our quality of life. Thank you for listening. KEIKO: Good morning, everybody. I am going to speak today in favor of the proposal. Limitless air travel inside Japan is a luxury that we can no longer MR. ROBERTS: Thank you to our two speakers. Now, are there any afford. The main reason is that it is extremely damaging to the questions from the audience? environment. The carbon gases produced by aircraft are very high and are a 頭人 proven cause of global warming. Therefore, we should try and reduce air 問1 次の(1)~(5)の文について, 本文の内容と一致するものには○.一致しないも travel as much as possible to protect the environment, not only for Japan but のには×を,それぞれ解答欄に記入しなさい。 also for the whole world. Secondly, air travel is actually unnecessary within the four islands of Japan. Now, while I appreciate that travel to Okinawa is (1) Keiko's main reason for opposing domestic air travel is the damage it a different case, there are efficient train services throughout Japan that are causes to the environment. h fast and environmentally friendly. These make an excellent alternative to air (2) Keiko thinks that air travel is cheap and efficient. flights, so there is really no need to use airplanes in most cases. Finally, (3) Keiko recommends that people travel between Okinawa and mainland there is an economic reason. Air travel is expensive for passengers because Japan by ship. the price of fuel keeps increasing, but airline companies are still struggling (4) Junko thinks that climate change is not an important problem. to make profits. Moreover, regional airports often cannot attract enough (5) Junko thinks that a lot of jobs will be lost if air travel is reduced. customers, and, overall, the industry is not cost-effective, It's time to admit that air travel is too damaging and expensive to be sustainable. Thank you. 問2 次の質問に英語で答えなさい。 Which of the two speakers do you more agree with? Give at least one JUNKO: Thank you, Keiko. I am going to disagree with the proposal for three reason for your answer. (解答欄:13.8cm×4行) reasons. Firstly, I think there is a strong economic case to support flying. Many jobs depend on air travel, not just the pilots and cabin staff, but also people who work in airports or for airlines, or who rely on fast transport.

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英語 高校生

全部答え教えて欲しいです

訓告に 別笛p.5--p.6 G①わ ん4:岳. gow Was your day? You look tired. B:Tam. Tve been on the ( ) ever since 1 left the house this morning. 1 just want to sit down and relax。 1 go 2 come 3 wake 4 step (⑳⑯@@@⑨) 2) rwont h ject i * i 1 nt say the project is totally ( ), but you'd better consider that it iS quite unlikely to Work well. 1 under construction 2 inahury と だ ⑪@⑥⑤6 3 with ease. 4 out of the question ・ (3) At first。 none of the guests spoke to each other, so their host broke the ( ) by getting eVeryone to play a game together. 1 tnme 2 ice 3 start 4 water ⑪9⑨96 G④ A: Do you know ifAunt j1 is planning to come and stay with us at Christmas this Year? B: As ( ) as 1 know, she's coming, but I haven't actually asked her. TIL call her tomorrow 1 long 2 soon 3 far 4 more ⑩990 h (GS) The president's explanation ( ) how the company fell into financial difficulties was 4 unmsatisfactory. 1 mcase 2 asto 3 due to 4 mthat ⑩@9⑨ (6) The couple decided to put ( ) their wedding for a couple of months after the bride's father suddenly entered the hospital for an operation. 1 up 2 out 3 off 4 to ⑩0@969 (7 Tn had been busy with work for the 1ast two weeks and hadn't had time to see his parents. So, he decided to ( ) by their house on the weekend. - 1 f 2 look 3 hold 4 drop ⑩@@ (18) _A: Whats the mafter wi you? You look Worried. B: Do you remember he vase that 1 ( ) to look after? Ibroke it by accident. 1 gave 2 wilbegiven 3 hasbeengiven 4 hadbeengiven [〈①@⑳人 lee after the meal. He usualy has 0M9M9MO ) smoking and (19) Jane asked John 下 he would coffee but requested ea 1 fo have 2

未解決 回答数: 1
英語 高校生

答え→4、4、3、1、2で合ってると思いますか⁇ 違うと思ったらどこがどう違うのか教えて欲しいです‼︎お願いします🤲

u an article to help you prepare for te jsh teacher gaVe 9 e co Englisl ith one of the comment S Your part O debate in the next class. 信 is shown beloW- 1のせこ ild's Roomn uorv @ amoe Of Chil Signifit By Cathy Becker | | | | s friends to their own room, | hild with a shared room. | 1 f this article Wr son said,“Tf a child invite: 品 than 8C de when 8 friend visits." Johnson | gs children | sharing 8 TOOT brin in reality is the opposite. The | Doctor Johni theyTl learn about manners faste Also, it give them a SenSe of pri also said, Many parents used to feel closer. Howeyer。 we know now that 8 ッ ]ack of personal SDace CauS8 conflict and argument8. | | Tn other words, children that have their own roomm are better at | nandling responsibility and mature 8OOn6r than children that dont. They can customize and choose what they want in their roorn。 glving hem control over their environment that teaches them about control and decision making. It also gives them: Self-confidenee, which is crucial for a child. It seems to be a comnmon trend to give them their own roonn as early in their childhood as possible. On the other hand, not all parentS agTee・ One parent said, “Contrary to recent popular belief, there are advantages to sharing 8 room. Children will learn to 匠6goti8te and commpromise Another parent added, “By sharing 8 rOOm children will draw a lne and take ownership of their belongings, Which is great for character building. Also, it helps them accept others and their differences.“ @ CommentS Ajieia Grant 了have 2 daughters and they share a room at the moment、One is neat and the oher js messy, so theyre always arguing! Were thinkmg ot

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