CMBUk smikar nigvismikar emeronti smikardwerkti manmyygbaøat lmhat;. KNnakenSamageRkam³ k> i 9 >. kmnt;témøa nig b énsmpabagerkam³. KNna + 9 k> 8+ i= a+ bi > a+ bi+ ( ) = i a+ bi 8 (a+ ) + (b+ ) i= + i X> = + i + i k> i ( ) i + 8 > ( + i) ( ) i X> ( + i) g> + i i + i i i+ i c> i i i+. edahrsaysmikaragerkam³ k> g> iy y+ i= c>. ekmansmikar + 8= Edlmanrws α nig β. β α KNna³ k> + > α + β 9 ( ) 8( ) = > y + + = 8 + = X> + = + α + β ( ) + ( )( ) ( ) =. ekman α nig β CarwsBIrrbs;smIkarageRkam³ k> ( 8)( 9) + ( )( ) = KNna ( α)( β) > ( + ) + ( + )( + ) + ( + )( + ) + ( + )( + ) = KNna ( α+ )( β+ ) 7. BUsumancMkarmYyerogctuekaNEkgmanTTwgesµInwg m nig benþay esµinwg m. Kat;cg;eFVIpøÚv myy CMuvijcMkarenaH eday[ TTwgpøÚvmanRbEvgesµI Kña ehiyépþrkladi EdlenAsl;BIeFVIpøÚvesµInwg Bak;kNþalépÞRkLa cmkar TaMgmUl. etibusurtuvykttwgpøúvrbevgbu:nµan? 8. eke)ah)al;myybikmbulgakartamtisqr. ry³ebl t vinatierkaymk )al;mankm<s; t t + + Em:tBIdI. k> rkry³km<s;gakarenah. > rkry³ebledl)al;etahysgakarrycføak;cuhmkvij. rkry³ebledl)al;føak;mkdl;di. - - - -
. KNnakenSamageRkam³ k> i 9 cmeliy i 9= i 9i = i ( i) = i i 9= i > i ( i) = = = i i + 9 i + =. i +. i 9 7 7 = i i + i = i i = i 7 7 = ( ) = 7 + = 9. kmnt;témøa nig b énsmpabagerkam³ k> 8+ i= a+ bi - 7 - - 8 - edaypþwm EpñkBit nig Epñknimµit eyig)an a= 8, b= > a bi ( ) a bi ( ) + + = i + + = i ( ) a+ bi+ i = i a+ bi+ i= i a+ + ( b ) i= i edaypþwm EpñkBit nig Epñknimµit eyig)an a+ = a= b = b= ducenh a=, b= (a+ ) + (b+ ) i= + i edaypþwm EpñkBit nig Epñknimµit eyig)an a+ = a = b 9 + = b= 9 ducenh a=, b= a+ bi 8 X> = + i + i eyigman a+ bi ( a+ bi)( i) a ai+ bi bi = = + i ( + i)( i) 9 i a ai+ bi+ b a+ b+ (b ai ) = = 9+ a+ bi a+ b+ (b ai ) a+ b (b ai ) = = + + i
. KNna enah a+ b (b ai ) 8 i eyig)an + = + edaypþwm EpñkBit nig Epñknimµit a+ b 8 = 8( ) a+ b= b a b a= ( ) = edahrsayrbbn ½eyIg)an a=, b= k> i ( ) i + 8 i ( ) i + 8= i + i+ 8i = i + 9i= 9i i ( ) i + 8= 9i > ( + i) ( ) i ( + i) = + i i = + i i ( ) = + ( ) ( + i) = + ( ) i = 9 i+ i = 9 i = 7 i ( ) i = 7 i i i X> ( + i) ( + i) = + i+ i + i = 8+ i + i i = + i i= + i ( + i) = + i g> + i i + i i + i i ( + i)( + i) i( + i) + = + i i ( i)( + i) ( i)( + i) + i+ 9i i+ i = + 9i i + i 9 i + i i = + = + + 9 + + i i + i+ i + 7i = + = = 7 = + i + i i 7 + = + i i i i+ i c> i i i+ i+ i i + i i + i i = = i i+ i i+ i i+ i ( i )( i+ ) ( i ) = + = + i i+ ( i )( i+ ) ( i+ )( i ) = + = + i i i i i i i + i i+ 8 i 8 = + = = i - 9 - - -
. edahrsaysmikar³ k> > i+ i 8 i = i i i+ ( ) 8( ) = ( ) 8( ) =,( )( 8) = ( )( 9) =, =, = 9 smikarmanrws =, = 9 9 y + + = 8 9 9 9 y+ + =, y+ = = i 8 8 7 7 y+ =± iy, = ± i 8 8 7 7 ducenh smikarmanrws = +, = + = X> y i y i 8 8 + =, + = + = + = =, = = ducenh smikarmanrws = + = + =, + = man = = = i i + i =, = i + i =, = ducenh smikarmanrws g> iy y+ i= c> iy y i + = man = = = i i i + i = = = = i, i i i = = = = i i i ducenh smikarmanrws =, = i i ( ) + ( )( ) ( ) = ( ) + ( )( ) ( ) = ( ) + + + ) + = + 9= = = 9 + =, = =, = + ducenh smikarmanrws. KNna³ β α k> + + α + β smikar + 8= manrws α nig β enah eyig)an - - - -
eyig)an > α + β b α+ β= = = a c αβ= = 8 a α+ β=, αβ= 8 ( + ) + ( + ) ( )( ) β α β β α α + = + α + β + α + β α+ β+ α + β = + α + β + αβ = ( α+ β) + ( α+ β) ( α αβ+ β ) + ( α+ β) αβ+ ( αβ) ( α+ β) + ( α+ β) ( α β) αβ + = + ( α+ β) αβ+ ( αβ) β α + ( 8) + = = = + α + β + 8+ 8 β α ducenh + = + α + β ( ) = ( α β) αβ + ( αβ) ( ) α + β = α + αβ + β αβ = α + β αβ = α + αβ+ β αβ αβ eyig)an α β ( ) ducenh α + β = 97. k> KNna ( α)( β) ebiαnig β CarwsBIrrbs;smIkar + = 8 8 = 97 ( 8)( 9) + ( )( ) = - - - - eyigman namegay ( 8)( 9) + ( )( ) = 7+ 7+ + = 9+ 9= eday αnig β Carwsrbs;smIkar enah b 9 9 α+ β= = = a c 9 αβ= = = 9 a ( α)( β) = ( β α+ αβ) > KNna ( α+ )( β+ ) eyigman = [ ( α+ β) + αβ] 9 9 = + 9 = (7 ) = 9= ducenh ( α)( β) = ( + ) + ( + )( + ) + ( + )( + ) + ( + )( + ) = ( ) ( ) ( ) ( ) + + + + + + + + + + = + + = eday αnig β Carwsrbs;smIkar enah b α+ β= = a c αβ= = a
namegay ( α+ )( β+ ) = α+ β+ αβ+ = ( α+ β) + αβ+ = + + = ducenh ( α+ )( β+ ) = 7. rkrbevgttwgpøúv tag CaRbEvgTTwgpøÚv SEFGH CaRkLaépÞenAsl; enahrklaépþtamgmulkw tambmrab; SABCD S EFGH= enah EF EH= eday EF= AB = EH= BC = AB=, BC= eyig)an S ABCD AB BC ( )( ) = ( )(8 ) = 9,( )(8 ) = + = ' = 9 = = 7 =, = 7+ 8. k>rkkm<s;gakarenah -kmbs;rbs;gakarkw esµinwgkmbs;edl)al;enartwm GaKar KWN³eBlt= eyigman h= t + t+, t= enah h= + + =, h= m > rkry³ebledl)al;etahysgakarrycføak;cuhmkvij -vakwcary³ebledl)al;eligdl;cmnuc<s;bmput Gtibrma eyigman h= t + t+ = + + t t 8 = + + = + ( t t 9) 8 ( t ) 8 h= t + ( ) 8 8 eyigexijfa enaebl t= kmm<s;gtibrmakw8m ducenh ry³ebledl)al;etahysgakarrycføak;cuhmkvij KWt= s rkry³ebledl)al;føak;mkdl;di -ry³ebledl)al;føak;mkdl;di KWeBlEdl h= eyig)an h= t + t+ =, t t = 7 ' = 9+ 7= t = + = 7, t = = < ducenh ry³ebledl)al;føak;mkdl;dikwt= 7s eday < enah = ducenh RbEvgTTwgKW= m - - - -
emeronti RbBn ½smIkar nigsmikardwerklmdab;<s; lmhat;. edahrsayrbbn ½smIkar³ k> + y+ z= y z= y+ z= + + = 9 y z + = 9 y z + = 9 y z + y= + y+ y = g>. edahrsaysmikaragerkam³ k> > X> g> + = 8 + = = + 8 + 9 8 = + = c> ( + )( + )( + ) = > + y= y + z = z+ = + y= X> + y = + y= c> 9 y = 8. kmnt;t;mélk EdlnaM[BhuFa p ( ) = 7+ k Eckdac;nwg ryc edahrsaysmikar p ( ) = etatamtmél k enah.. BhuFa p ( ) Ecknwg mansmnl; ehiy Ecknwg mansmnl;. rksmnl;enaebledl p ( ) Ecknwg ( )( ). ekmansmikar + a + b=. edaysáal;rwsmyyénsmikarkw + i curkmnt;tmél a nigb rycedahrsaysmikartam tmél a nigb enah.. ek[ + CaktþaénBhuFa f ( ) = + a + b+ a+ b. currktmél a nigb.. kmsanþcamyyknitvitüa bursbinak;)an culetakñúghaggaharmyy. cmnayetaeligaharmyy eblenah KWGs;cMnYn duløa. BYkeK)anecjluymñak; duløaetaeligaharenh. GñkbMerI )anyk luy duløaenhetaegaym as;hag Etedaym as;hagsáal; burstamgbikat;k¾egaygñk bmeriykluy duløa etaegayburstamgbivij. eday mankmnitminesµahrtg;gñkbmerirbkl; egayburstamgbirtwmetduløabu:enañh ehiy duløa etotkwtukkñúgehae)a:øünég. eblenh burstamgbirtuvcmnaymñak;rtwmet duløab:uenñah srubetatamg binak; cmnaygs; duløa ehiyebibenßm duløa EdlGñkbMerIkwbenaH KW TaMgGs;duløa. smnyrsyrfaluy duløaetot)at;etana ebiluycmnaydmbuggs; duløa enah? - 7 - - 8 -
. edahrsayrbbn ½smIkar³ k> + y+ z= y z= y+ z= -yk( ) buk ( ) cmeliy smmulnwg eyig)an z= ( a) -yk( ) ( ) ( ) + eyig)an + y+ z= ( ) y z= ( ) y + z = ( ) y+ z = ( ) + + y + z = ( ) ( ) + z= ( b) tam ( )&( ) a b eyig)anrbbn ½ z= ( a) z= ( a) smmulnwg + z= ( b) + z= ( b) z= ( a) + z= ( b) 7=, = yk = CMnYs( ) z=, z= = a eyig)an yk =, z= CMnYs( ) + y+ =, y= = eyig)an ducenhrbbn ½smIkarmanrws =, y=, z= > + y= y + z = z+ = smmulnwg yk ( ) ( ) ( ) + y= ( ) y + z = ( ) z + = ( ) + + eyig)an ( + y+ z) =, + y+ z= 7 (*) -yk( ) CMnYs ( ) - yk ( ) CMnYs ( ) - yk ( ) CMnYs ( ) * eyig)an + z= 7, z= * eyig)an + = 7, = * eyig)an y+ = 7, y= ducenhrbbn ½smIkarmanrws =, y=, z= + + = 9 + + = 9 ( ) y z y z + = smmulnwg 9 + = 9 ( ) y z y z + = 9 9( ) y z + = y z tag X=, Y=, Z= enaheyig)an y z X+ Y + Z= 9 ( ) X Y + Z= 9( ) X+ Y Z= 9( ) -yk( ) ( ) + eyig)an X+ Z= 8, X+ Z= 9( a) -yk( ) ( ) + eyig)an - 9 - - -
X Y + Z= 9 ( ) + X + Y Z = 8( ) X Z= 9, X Z= ( b) tam ( )&( ) a b eyig)an X+ Z= 9( a) X Z= ( b) yk ( a) ( b) eyig)an Z=, Z= CMnYs ( ) X =, X= yk X, Z eday X> = = CMnYs ( ) + Y = 9, Y= 9= X= = = Y= = y= y Z= = z= z b eyig)an ducenh RbBn smikarmanrws =, y=, z= + y= + y = smmulnwg + y= ( ) + y = ( ) tam ( ) eyig)an + y=, y= CMnYskñúg ( ) + ( ) = + + = =, ( ) = =, = -cmebah = CMnYskñúg ( ) -cmebah = CMnYskñúg ( ) )an + y=, y= )an + y=, y= ducenhrbbn ½smIkarmanKUcMelIy, y + y= y smmulnwg g> = = rw =, y= + = ( ) + y+ y = + y+ y = ( ) tam ( ) eyig)an + y=,y= y, = CMnYskñúg ( ) + + = + 9 + ( ) + = -cmebah = CMnYskñúg ( ) -cmebah = CMnYskñúg ( ) + =, + = =, = ( a+ b+ c= ) )an + y=, y= )an 9+ y=, y= ducenhrbbn ½smIkarmanKUcMelIy, y + y= y + = smmulnwg c> = = rw=, y= ( ) 9 y = 8 9 y = 8( ) eyig)an y,y y, 9 = 8 9 ( + 9 ) = 8 tam ( ) + = = = CMnYskñúg ( ) = 8, = = - - - -
-yk = CMnYskñúg ( ) )an y y + =, = = ducenhrbbn ½smIkarmancMelIy =, y=. edahrsaysmikaragerkam³ k> + = + =, + + = ( ) ( ) + ( ) = ( )( + ) =. =, =. + = = = 7= 7i + 7i 7i =, = i i + =, =, = ducenhsmikarmanrws 7 7 > 8 + = cmebah = eyig)an ducenhsmikar man Caktþa eyig)an ( ) 8 + = = CarwsmYy enah smikarman 8 + =, + + = ( ) ( ) ( ) = ( )( ) =. =, =. = = + = 9 + 7 7 = =, = = =, =, = ducenhsmikarmanrws = tag t t t = enaheyig)an = ' = + = t = + =, t = =. t= =, =±. = = =, =± t i i ducenhsmikarmanrws ( =±, =± i) X> + 8 + 9 8 = cmebah = eyig)an + 8+ 9 8 = smikar man= CarwsmYy enah smikarman ( ) Caktþa eyig)an + 9 9 + 8 8 + = ( ) + 9 ( ) + 8 ( ) + ( ) = ( )( + 9 + 8+ ) = ( )( + + 8 + 8+ + ) = ( ) ( + ) + 8 ( + ) + ( + ) = ( )( + )( + 8+ ) = - - - -
. =, =. + =, =. + 8+ = ' = = = +, = ducenhsmikarmanrws ( =±, = ± ) g> + = tag t t t = enaheyig)an + = ' = = 8 t = 8+ 8= 8+, t = 8 8= 8. t= 8+ =, =± 8+. t= 8 =, =± 8 ducenhsmikarmanrws ( =± 8+, =± 8 ) c> ( + )( + )( + ) = ( + )( + )( + ) =, [ ( + ) ][( + )( + ) ] = ( )( ) + + + = tag t= + eyig)an tt ( + ) =, t + t = ' = + = t= + =, t= =. t= = +, + = =, =. t= = +, + + = = 9 = = i + i i =, = i ± =, =, = ducenhsmikarmanrws. kmnt;t;mélk EdlnaM[BhuFa p ( ) = 7+ k Eckdac;nwg p ( ) Eckdac;nwg luhrtaet p () = eyig)an p () = 7 + k= + k=, k= ducenh k= -edahrsaysmikar p ( ) = etatamtmél k eday k= eyig)an p ( ) = 7+, ( ) 7 + = ( )( ) = p = enah + + = ( ) ( ) ( ) = - - - -
. =, =. = = 9+ = 9 + 7 7 = =, = = ducenh smikarmanrws ( =, =, = ). rksmnl;enaebledl p ( ) Ecknwg ( )( ) eyiggacsresr p ( ) Carag p ( ) = ( )( )( q) + a+ b - p ( ) Ecknwg mansmnl; enah p () = p() = ( )( )() q + a + b= a+ b= a+ b= ( ) - p ( ) Ecknwg mansmnl; enah p () = p() = ( )( )() q + a + b= a+ b= a+ b= ( ) tam ( ) nig ( ) eyig)an a+ b= ( ) a+ b= ( ) yk ( ) ( ) eyig)an a, a ( ) + b=, b= = = CMnYskñúg namegay p ( ) = ( )( )( q) + + ducenh smnl;énkareck p ( ) nwg ( )( ) KW+. kmnt;tmél a nigb -eday + icarwsmyyénsmikar eyig)an ( ) ( ) ( ) + i + a + i + i + b= ( ) ( ) ( ) ( ) i i a( i ) i b ( a ) i ( b a ) + a + b= enah + i + i + i + a + i i+ b= 9+ + + = + = eyig)an a a= a= = b a = b = b= ducenh a=, b= -edahrsaysmikar + + = + + = + + + = ( + ) ( + ) + ( + ) = ( + )( + ) =. + =, =. + = ' = = = i = +, i = i ducenh smikarmanrws ( =, = +, i= i) - 7 - - 8 -
. rktmél a nigb -eday + CaktþaénBhuFa f ( ) = + a + b+ a+ b enah eday eyiggacsresr eyigman f ( ) = ( + )( q) + = + = ( ) + ( ) = ( )( + ) enah f ( ) ( ) ( ) q ( ) = + eyigman f() = ( ) ( + ) q() = f( ) = ( ) ( + ) q( ) = f ( ) = + a + b+ a+ b namegay f a b a b () = + + + + = a+ b+ 9=, a+ b+ = ( ) f( ) = ( ) + ( ) a( ) + b( ) + a+ b = -tam ( ) ( ) a b+ 7= ( ) & eyig)an a+ b+ = ( ) a b+ 7= ( ) -yk( ) ( ) 8 + )an a+ 8=, a= = CMnYskñúg ( ) + b+ =, b= ducenh a=, b= - 9 -