なんで式変形でこうなるのか教えて欲しいです

(1) 複素数2, wに対して、不等式 [z+a]s[z]+[mr]が成り立つことを示せ. 3 絶対値,極形式(証明問題) (2) 複素数平面上で、原点を中心とする半径1の円周上に3点. i.yがある.ただし, α+β+y=0 とする. (a) 等式 |aß+By+ya|=1 =1が成り立つことを示せ. a+B+r (b) 不等式le(8+1)+8(y+1) +y (a+1)2la+8+y| が成り立つことを示せ (富山大・理(数) -後) 例えば|a|=1という条件が与えられているとしよう。このとき ( a を αで表せる) a 絶対値の条件式の扱い方 •|α/2=1であるから、 aa=1, ●α = cos0+isin0 とおく. ●|By|=kaBy|=k などという使い方がある. 絶対値の等式, 不等式の証明 してみたりしよう. そのままでは変形しにくいときは、両辺を2乗したり、極形式で表 ■解答量 (1) z=r(cos0+isin0), w=R(cosy+ising) (≧0, R≧0) とおくと, |z+w|=|(rcos0+Rcosy) +i (rsin0+Rsing) | =(rcoso+Rcos)+ (rsin0+Rsing)2 cossint) +2rk (costcosy+sinosing) +R2(cos2p+sin') =r2+2rRcos(0-9) +R2 ≦r2+2rR+R2=(r+R)2=(|z|+|w|) 2 2+w|≦|2|+|w| (2) (a) a+By+ya]-[a+8+yl① を示せばよい。 ||=|8|-|r|-1により, [a8yl-1.1. BF-1 Yy=1であるから, \aB+ By+ya] [aB+By+ya][aB+By+ya||1 \aB+By+ya|=- laby| aBy 1 + + a B ■P(z), Q(z+w) とおくと,wは PQ を表す複素数で,下図の ようになる. AOPQE |z+w| Q(z+w) 辺を考える 1001 と (1) 成 立 0 || この両辺を2乗した式を示して もよいが、ここでは工夫してみる。 =1により1/27 -ly+a+B[-ly+a+ 8[-]y+a+8 したがって、題意の等式が成り立つ. (b) la(8+1)+8 (y+1)+y (a+1)=(a+by+ra)+(a+8+z)] ...) (1)で, z=aß+By+ya, w=a+β+y とおくと, ①により|2|=|w|で, ②-|z+g_n_z]+[]-[g]+[s[-2]]=2la+8+yl . \α(B+1)+B(y+1)+y (a+1)| 2|α+B+yl 3 演習題(解答は p.113 ) |2|-|za|-|za|-1 をみたす三つのに対して、+230 B=z1zz+228 とおく。 (1) =y となることを示せ. (3)の分子は (2) Y |α|=|8|となることを示せ. Z」の対称式だから、 (Z1+Z2)(22+23)(23+21) (3) z=- 212223 は実数であることを示せ. (宮城教大) B, yで表せる. 2+22α-z」 などとし よう。 100

英語 askに3単現のSがないのは何故ですか？

[] he often forgets something and ask me or my mother (10)

否定の問題です。教えてください。

1.次の文の( )に入る適当な語句を①~⑩から選びなさい。 (1) A: I went to Hokkaido and Okinawa last year. B: That's wonderful. I haven't had a chance to visit ( ) of them. either none (2) My grandfather is a heavy smoker, but he ( usually [大阪産業大 *〕 some ①ever ) drinks. ③mostly nearly (大阪学院大) ). I must be back by 8 o'clock." not [南九州大] seldom (3) "Can't you stay a little longer?" "I'm afraid ( so yes 3 now (4) "I'm sorry, we have ( ) rooms available at the moment. Why don't you try another hotel?" any no (5) It was so dark that we could ( [日本大〕 none nothing ). hardly see see hard see hardly [大阪経済大 ] )" Neither do I. So do I. 〔京都産業大] hard to see (6) "I rarely go to concerts these days." "( I don't, neither. I do, too.

動名詞、不定詞についての問題です 解いてみたのですが、間違っていたら教えてほしいのと、なぜそうなるのか教えていただきたいです🙇🏻‍♀️💦 あまりよく分からないところなのでお願いします(><)

3.[ ]内から適切な語を選び、必要なら形を変えて、対話文を完成させなさい。 (1) A: I'm thinking of watching checking B: I saw it. It wasn't all that great. Spielberg's latest movie. my smartphone all the time. (3) A: Would you (mind) (2) A: I have a bad habit of B: I know what you mean. I do it, too. turning going B: Sure. No problem. (4) A: Do you remember B: Of course. I'll never forget that day. down the TV? (2点×5=10点) to the art museum with me last year? (5) A: You forgot not having closed your bedroom window last night, didn't you? B: Yes. And as a result, I caught a cold. [go/watch/turn/close / check ] [ go /

動名詞、不定詞についての並び替え問題です 解いてみたのですが、間違っていたら教えて欲しいです！ 明日テストなのでよろしくお願いします🙇🏻‍♀️

2. ( )内の語句を並べかえて, 英文を完成させなさい。 ただし, 下線部の動詞は適切な形にすること。 緊張した (1) I (enter / nervous/was/about/very) the teachers' office. I was about nervous very entering. (2) Sarah (of /in/proud/is/ appear) a movie last year. Sarah is proud appearing in of (3) (forget / never / treat / in / I'll) an unfair manner in that country. I'll never forget to treat (2点×3=6点) the teachers' office. a movie last year. In an unfair manner in that country. 「切り

1文目って第3文型の倒置でしょうか

V- 2 There are more solid studies (recently) [that looked at people [clinically diagnosed with insomnia disorder], (rather than self-described poor sleepers)]," agreed the University of Pittsburgh's Christopher Kline, [who studies sleep S V (through the lens of sports medicine) ]. The results show (exercise 両方で データ表現 improves both self-reported and objective measures of sleep quality, [such as (what's measured (in a clinical sleep lab)>])." 具体例の目印

黄色丸で囲ってあるitが何を指すのか教えてほしいです

$49.99 BB Green Spinner For customers concerned with the environment, we offer the Green Spinner, which uses 40 watts of electricity on its normal setting. On the "green" setting, it uses under half that! The fan can rotate 180 degrees, giving it excellent coverage for a small room of around 75 square feet. If it breaks, replacement parts are available at low cost in our online store, and you get a special deal on replacement parts if you use our coupon codes.

下線部③を並び替えてください。という問題なんですが、どのように考えたらいいのか分かりません。 教えてください！

19 Read the passage and answer the questions. ORG OF US. udma2 to enoitelugo Imagining locations for a wedding, people think of churches, 008 00 hotel chapels, or even a beautiful beach or park somewhere. However, there are ①many more fantastic and unusual places where wedding planners can arrange the perfect day for couples 5 who want something a bit different. 0001 Located deep underground, the National Showcaves Centre for Wales can provide a stunning background to a wedding ceremony. There is a huge section in the caves called the "Dome of St. Paul's," which includes two waterfalls flowing into a large lake. 10 The cave's natural and romantic setting ②could make a wedding truly special. 009 008 00% QHints aros chapel [tfæpǝl] 礼拝堂, チャペル the the ocean. stunning [stániŋ] とてもすばらしい cave [kéiv] than waterfall [wó:tǝrfò:]] 008 00 spectacular [spektækjulǝr] 壮観な As some people might not want to marry in a cave, a company 008 in New Zealand offers a wedding ceremony in a spectacular outdoor setting. The company will fly couples and their guests by 15 helicopter to the top of a mountain. Looking at the amazing fuquq ow! T panorama of mountains, lakes and rivers, lovers ③[ will become might their wedding / how / easily imagine ] one of the most memorable days of their lives.nd 20 a (S) atos Even more adventurous couples can get married underwater. 20 Putting on scuba gear, the couples descend to a depth of 15 gear [giǝr] meters in the sea off the coast of Trang province in Thailand. Of course, exchanging wedding vows underwater is difficult, so they T 25 need to use a series of diving hand signals, ending with an "OK" sign to indicate "I do." As well as these locations, there are thousands of other places around the world that can offer lovers an alternative to the tradition of walking down the aisle. Perhaps f future weddings will be held in space, on the moon, or even on Mars. (269 words) 『リーディングに役立つ英文法-ENGLISH CHALLENGER」 Kyoko Okamoto, Benedict Rowlett Aya Kinoshita, Sara Ellis*** descend [disénd] b off the coast of ~ ~沖で Trang province in Thailand タイのトラン県 vow [vȧu]) pninatai.l aisle 通路 onsiquis el lliw omi) indW (S)

1枚目の写真の下線2の補足説明である、2枚目の写真についてなのですが、青い波線で引いているところはなぜそうなるのですか？

もわかっている場所と考え、 the seashore [the shore/thebeanとして Alessi s jad 19qaqawon odd ni bax I gmi Our society is aging [ageing graying / (*) 1 ingreying/ X getting old] rapidly [quickly] (,) and the 2 number of young workers [young laborers / young members of the workforce] is [× are] steadily Todman sds to a sdj ni basi I [gradually] decreasing. sablat] gainsbay al yddod saodw [slqosql 3

当てはまる単語を教えてください！

benefit (noun) OPAL Something that is good or helpful escape (verb) to get free from someone or something except for (adverb phrase) without; excluding forget (verb) to stop thinking about something; to not remember patient (adjective) have problems protect (verb) able to stay calm when you are waiting or when you OPAL to keep safe some kind of (phrase) a type of