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数学 高校生

丸で囲ってるところ どうやって1を出したのかがわからないです。

1のn乗根と TC 例題61 COS の値 n 2 ²/²z+ 2 -π+isin π とする。 57 a = cos 5 (1) α°,1+α+α² + α°+α, 1 +α +α + α+ (α) の値を求めよ。 2 (2) cos 15 の値を求めよ。 (1) ド・モアブルの定理を用いる。 1+α+a²+a+α* 因数分解 1=(x-1)(x+x+x2+x+1)を利用。 前問の結果の利用 αと αα = |α|2 を利用 の関係 → 1+α+α²+a+ (α) をつくる。 Action》 α-1 +α - 2+ +α+1は,α-1の因数分解を利用せよ (②2) cos/2/3=(axの実部 COS この式で COS / πを表すと? α, Action》αの実部は, 1/12 (α+α)を考えよ 5 (1)=(cos = (cos-²/+isin / )* = cos2π+isin2=1 5-1=0 これより よって (α-1)(a^ + α + α² +α+1)=0 _ αキ1 であるから 1+α+α°+α°+ α = 0 1 |a| = 1 すなわちad = 1 より, a であるから a 1 1 1+a+a² + a + (a)² = 1 +a+a² + + amica² 18(1 1+a+a² + a³ + aª = 0 a² 2 2 (2) x = cos- -π とおくと, COS 1/1/(a+α)である 5 から α+α = 2x また a²+(a)²=(a+α)²-2aa =4x²-2 (1) より, 1+ (a+α)+{a²+(a)^}=0であるから, ①, ② を代入すると 4x2+2x-1=0 2 −1+√5 4 x = COS π>0 であるから cos= 5 2 α = COS 02/77 + in / π+isin πとする。 (1) ° + α5 + α* + + α + α+1の値を求めよ。 (2) 3+ (α)+α²+(a)² + α + α + 1 の値を求めよ。 (日) 2 思考プロセス 練習 61 九三 ド・モアブルの定理 一般に x" - 1 =(x-1)(x-1+xn-2 +・・・+1) 2 lal = COS n+isin 12/31 =1 19 1 +α+α² + α3 + α = 0 を代入する。 aa = |a|=1 1±√5 4x= 4 0 < =² / π < / kh 2 0<cos / <1 27/10 034²-4x=1 であることを示せ。 2章 複素数平面

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英語 高校生

日本語に翻訳してくれる方いらっしゃいますか😭

F UXIT How many hours of sleep did you get last night? For years, scientists have tried to work out how long we should sleep to help our bodies and minds to function best. In 1951, two researchers at the University of Chicago made a breakthrough by identifying an important stage of sleep called REM sleep. 5 REM is an abbreviation for Rapid Eye Movement and the name comes from 由来する。 AFG the very fast movement of the eyes during sleep. In REM sleep, the brain is active but the body is asleep. When a person is having dreams they are often in REM sleep. During this time, the eyes might move quickly in reaction to something seen in a dream. Someone in REM 10 sleep may wake up suddenly to a noise and be able to remember the dream in detail. ju While REM sleep is known as the body's sleep, non-REM sleep is known as ryhmis the mind's sleep. During non-REM sleep, the brain relaxes while the body produces growth hormones so it can recover. About 80 percent of sleep is lat 15 non-REM sleep. If you sleep for seven to eight hours a night, only about one and a half hours are spent in REM sleep. In one night, a person will continue to repeat a cycle of both REM and non-REM sleep, which lasts about 90 NEXU prinsteil minutes. HO Many people will repeat about five cycles each night to help them function 4 people 20 best. However, other people may need to repeat (fewer or more cycles. Interestingly, while Leonardo Da Vinci only slept for about 90 minutes per おりりない day, Einstein needed ten hours of sleep. Still, both of them became famous 海 for their artistic and scientific achieveme achievements. Perhaps they were getting just the right amount of rest for their bodies and minds(aby) 116 for their artistic and scientific の 95. godinu b many more most bady brain nch

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