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week4 - 4— Honwaems Ewafims a,” U Cal(ed er £n‘vd...

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Unformatted text preview: 4—. Honwaems Ewafims a,” + + U. Cal/(ed er £n‘vd soiufim 302m. TL‘C Ma “Wed mot-n3: 1‘s -~ I I I i o A "‘ 1 2. 1 E o 2 3 z? {3‘9R3‘2Rs O l 0 o 0 I o o ’-—-———-——9 a" 0 I 0 o] O o o o RIQRV7RL O ._..__.9 ¥ 0 ' 0 II? 0 o 0 0 o o ‘ 71M; — Thecfem 2.2. [ A “{LO moaenems s iaéfiem Solution or (A: {has Wm?) mama Swims; i ! flare ME: T10 OHM/r“ foSSEEHEEQy (has ‘H’tf’, “EVE/fat AH?ch B ComElex numbens " Comrlex Walkers, V ‘ ‘ mar/4 W’ex number Is a, manbem of H18 Dem #4213 e a and b W6 Feafl members / and 75 £5?me (CM 't’m/awy number”) 10% He fro!)th 2 432—4. (m M) (c + c155:>+,{,(b+d) (a,+ bi) -~ (C+ 2, (a._c)+/i(b-0[) Examfle I. ‘ v Let %:-2,+/E and w:1-———4:. 415.14 Em Ew:(:_2_+/C>(t~x{) =(—-2+2A‘.3 +(,£——/Lz) - "ZNZA‘ + xi—(-~I) 2 "i +3/{L 4 ‘ , The arm The a“ k 361178, f M 0 adj: . E 60f ‘Z‘ _a+ib ) de 0 0T8 at b 35/ K ~1+2£ ‘ 3~4f SAk” 'Z::”;:ZZ” 3*44 <-l+2£ )(3'441) — §+4L .L - *3+4~L+6/C ~84 25 "3 WM, +65 -—-8 (-4) @2123! c0552! , 19-21%! sings a = 1%! (@5326 + ism) cad/(ed 5L POIa/Vfom °§ 5‘ . ~ ~ \ - 4 may . “Mama uh; gammy a? £1 £2 =3 (COS ¢I +’CS‘;‘¢I) 1:554552) 4241a; (Cos(¢,+¢z)+’fSl;\C¢g+¢z)) I ‘E‘W\e?£xfre55 Z=(l+/L)(l”i\f§/L) {n 070_1W§°m' moo-5» =252(c»s(%¥~%> “WE-3%)) awed—1.5) +;s.;\(»%)) Exmkfleslf 2,:—-1+,J§/L and £22“!+/C Wresg 722%.z; fin fola/rfarm mun/Ra 5&5 Frv‘nczfafi augment. W“: z‘ = 266%) Haw-31>) ZZ— ) H49 'C \‘ JUNE w 'Jt’f‘ejftme J I? De Moivre/S Theorem 0 £:IE‘<COS¢+’ESI}\¢) and 13} TL ‘34 17‘”thC integer , filefl 27771 :[%!n(Cos 71525 +475an¢) Infach I): 1} “true for negative integers or “:0 (when. (z‘aFo) . 50/ «gm U7: < De HoWreflkw Wt“— 3 MdtfiCej Md Md/fn‘x Aldebm Sachem}! Oferwtims cm. Matrices l. Mmtfice; A Matrix is an mm (771 b5 70 mg of number; I added Midas or damn/t5 an “:2 am a“ an am m1 amz am We com denote a, Mfix b3 A :: (afixnxn . We also C“ILA av mmtrfx a Size mm, Mnem 1:1, an mxt maier F5 eat/Med 6L Wamfifix (or W“ vedtor). If flacoflwf‘m5 of Azaliflmxn (V6 erotors (1,, a2) an, Hum toe m3 refresent A a; A £6173 Matrix IS an mxn mmtrik whose Wigs Examfle the, 4x5 matrix A wdikenirfej “a; xiv-*3 (Z) Mairfx AJoLOHm and Secular M41509] motion 1 z ,. h .. ' Def: A (613)!"an / B “‘ (bLCPmKn £74 11' (é‘lg)mxn ,‘lx‘caflbfl (3) Mam< M53 61er a” an @211 ' am". TYLer 2 ml am . . . Ln» b” biz . bar B 52! 1’22 1 : é 0315(723 mx r' 02“ s 2 3 I 0 ' 5 ; AB: Lil, 5’ 6 0 O O n; 3 fl ,4 0 S ’(xoafzaco43iw0 MI +Z‘*0+3*I y*i+2*0f3*61) 4*i+5«*o+6¥(?i) 4-¥'o+5*0+6*0 +*i+'5*0+é*f y, Jrgaeo-rwéi) ~¥*’0*8*0*7*0 7H +8“) +77H 0 4 :2 0 IO 0 /6, O" (23 23A :: 0 (3,] [‘7‘ 5‘ a] 0’ :Lga, 8/012 : 0 0 0 6 6 6 ...
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