Ukuqonda Umsuka Wezinombolo Eziyinkimbinkimbi
Umkhakha wezibalo ugcwaliswe ngemibono, ngaphandle, ebonakala ingabonakali futhi iphikisana, ize ivele iziveze njengezinhlaka ezinhle kakhulu nezibalulekile zokuqonda umhlaba. Omunye umqondo onjalo yilowo wezinombolo eziyinkimbinkimbi. Lezi zinombolo, ezihlanganisa kokubili ingxenye yangempela kanye nengxenye ecatshangelwayo, zingase zibonakale zingavamile ekuqaleni. Kodwa-ke, zinezimpande ezijulile emlandweni wezibalo futhi zidlala indima ebalulekile ezindaweni ezahlukahlukene njengobunjiniyela, i-physics, kanye nokucubungula izimpawu. Ukuze uqonde ukubaluleka kwazo, kubalulekile ukulandelela imvelaphi yazo nokuqonda intuthuko yazo.
Ukuqala Kwezinombolo Ezingokomfanekiso
Indaba yezinombolo eziyinkimbinkimbi iqala nge-quadratic equation. Kusukela ezikhathini zasendulo, izazi zezibalo ziye zaxazulula ama-equation efomu \(x^2 + bx + c = 0\). Kodwa-ke, izixazululo ezihilela izimpande zesikwele zezinombolo ezingezinhle zisalokhu zingaqondakali futhi ziyadida. Isibonelo, isazi sezibalo sasendulo samaGreki uDiophantus saphawula izixazululo ezihilela izimpande zesikwele ezingezinhle kodwa sazilahla njengezingenakwenzeka. Ngokufanayo, cishe ngesikhathi esifanayo, izazi zezibalo eNdiya naseShayina zahlola ama-equation e-polynomial, zithola izimpande ezingezinhle ziyinkinga.
Kwaze kwaba ngekhulu le-16 lapho isazi sezibalo sase-Italy uGerolamo Cardano senza khona intuthuko ephawulekayo. Emsebenzini wakhe obalulekile u-Ars Magna (1545), uCardano wethula ifomula yokuxazulula ama-cubic equation. Ngesikhathi esebenza kulezi zibalo, wahlangana nezimpande zesikwele zezinombolo ezingezinhle. Nakuba ayengabaza ukwamukela lezi zixazululo ngokugcwele, akazange azilahle ngokuphelele. Kunalokho, waphawula ukuba khona kwazo futhi waze wazisebenzisa ngokwe-algebra, wabeka isisekelo sezazi zezibalo zakamuva sokuhlola lezi zinombolo 'ezicatshangwayo' ngokungathi sína.
Intuthuko ngekhulu le-17 nelama-18
Igama elithi "imaginary" laqanjwa nguRené Descartes ngo-1637, ekuqaleni elalihloselwe ukuba igama elihlambalazayo ukuchaza la manani abonakala sengathi ayinganekwane. Kodwa-ke, leli gama lanamathela futhi kancane kancane lalahlekelwa incazelo yalo yokudelela. Phakathi naleso sikhathi, intuthuko yaqhubeka njengoba izazi zezibalo ezifana noRafael Bombelli zaqala ukuchaza nokusebenza ngokuqinile ngalezi zinombolo.
Umsebenzi kaBombelli wawubaluleke kakhulu. Encwadini yakhe ethi Algebra (1572), uBombelli uchaze imithetho yokulawula izinombolo ezicatshangelwayo. Wabonisa indlela yokwengeza, ukususa, ngisho nokuphindaphinda lezi zinombolo, ngokuyisisekelo ethuthukisa i-algebra yokuqala yezinombolo eziyinkimbinkimbi. Umsebenzi kaBombelli wawubalulekile ekwenzeni umqondo wezinombolo ezicatshangelwayo uthakazelise umphakathi wezibalo.
Ukwamukelwa nokuqonda okusemthethweni kwezinombolo eziyinkimbinkimbi kwathola ukukhushulwa okukhulu ngekhulu le-18 ngeminikelo yezazi zezibalo ezifana noLeonhard Euler noCarl Friedrich Gauss. U-Euler waba nendima ebalulekile ekumeleleni izinombolo eziyinkimbinkimbi ngesimo sama-exponents. Wethula inothi \(i\) lomsuka wesikwele ka--1 futhi wasungula ifomula ka-Euler edumile \(e^{ix} = \cos(x) + i\sin(x)\), ekhanyisa ukuxhumana okujulile phakathi kwe-trigonometry kanye ne-complex exponentiation.
Umsebenzi Wokuqala KaGauss
Ngesikhathi u-Euler eqala isiteji, kwakunguGauss owanikeza isisekelo esiqinile sezinombolo eziyinkimbinkimbi. Ekuqaleni kwekhulu le-19, uGauss wafakazela i-Fundamental Theorem of Algebra, ethi yonke i-non-constant polynomial equation inomsuka owodwa okungenani oyinkimbinkimbi. Le theorem yagcizelela ukuphelela kwezinombolo eziyinkimbinkimbi ekuxazululeni izilinganiso ze-polynomial futhi yaqinisa indawo yazo ku-theory yezibalo.
UGauss uphinde wethula ukuchazwa kwejiyometri kwezinombolo eziyinkimbinkimbi. Wamelela izinombolo eziyinkimbinkimbi njengamaphuzu endizeni, manje eyaziwa ngokuthi indiza eyinkimbinkimbi noma indiza i-Argand (eqanjwe ngoJean-Robert Argand naye owayichaza ngokuzimela). Inombolo eyinkimbinkimbi \(a + bi\) ingabonakala njengephuzu elinama-coordinates (a, b), lapho \(a\) iyingxenye yangempela kanye \(b\) yingxenye ecatshangelwayo. Lokhu kumelwa kwejiyometri kunikeze izindlela eziqondakalayo zokuqonda imisebenzi yezinombolo eziyinkimbinkimbi, njengokuhlanganisa, ukususa, kanye nokuphindaphinda.
Izinombolo Eziyinkimbinkimbi Enkathini Yanamuhla
Ngokusekelwa kwesisekelo kuka-Euler noGauss, izinombolo eziyinkimbinkimbi zaba yingxenye ebalulekile yezibalo futhi zathola ukusetshenziswa emikhakheni eyahlukene yesayensi. Ku-physics, ikakhulukazi ku-electromagnetism kanye ne-quantum mechanics, izinombolo eziyinkimbinkimbi zibalulekile. Isibonelo, umsebenzi wamagagasi ku-quantum mechanics uchazwa kusetshenziswa izinombolo eziyinkimbinkimbi, okwenza kube lula ukubala amathuba kanye nencazelo yezakhiwo zamagagasi ezinhlayiyeni.
Kubunjiniyela, ikakhulukazi kubunjiniyela kagesi, izinombolo eziyinkimbinkimbi zisetshenziselwa ukuhlaziya amasekethe e-AC. Onjiniyela basebenzisa umqondo wama-phasor, okuyizinombolo eziyinkimbinkimbi ezimele imisebenzi ye-sinusoidal, ukuze kube lula futhi kuxazululwe ama-differential equation alawula ukuziphatha kwesekethe. Le ndlela iyisisekelo ekuklameni nasekuqondeni izinhlelo ezifana nemisakazo, omabonakude, kanye namagridi kagesi.
Ngaphezu kwalokho, ekucubungulweni kwesignali, kusetshenziswa izinombolo eziyinkimbinkimbi ekuhlaziyweni kwe-Fourier—indlela yezibalo ehlukanisa imisebenzi noma izimpawu zibe amaza. Lokhu kubalulekile kubuchwepheshe obuningi, okuhlanganisa ama-algorithms okucindezela umsindo nezithombe njenge-MP3s kanye ne-JPEGs.
Uhambo Oluqhubekayo
Uhambo lwezinombolo eziyinkimbinkimbi kusukela kokungavamile kwezibalo okumangalisayo kuya ekhoneni lesayensi yanamuhla nobunjiniyela luwubufakazi bamandla okucabanga okungabonakali. Lokho okwaqala njengomzamo wokuxazulula izibalo ezazibonakala zingenakwenzeka kwaholela ekuthuthukisweni kohlaka lwezibalo olunemiphumela ebanzi.
Namuhla, ucwaningo lwezinombolo eziyinkimbinkimbi luyaqhubeka nokukhula, luthonya izindawo ezifana nethiyori ye-chaos, i-fluid dynamics, kanye nethiyori yezinombolo. Ukuhlola izakhiwo zazo akunikezi ukuqonda kuphela ngezimo zezibalo kodwa futhi nasemhlabeni wemvelo nowobunjiniyela. Izinombolo eziyinkimbinkimbi zisikhumbuza ukuthi ukuphishekela ulwazi kuvame ukuqala ngokwamukela okungaziwa nokubuza okungenakwenzeka.
Empeleni, imvelaphi kanye nentuthuko yezinombolo eziyinkimbinkimbi kuyisibonakaliso sohambo olubanzi lwemicabango yezibalo. Kusukela ekuzabalazeni kwezazi zezibalo zasendulo ezibhekene nezimpande ezimbi kuya ekuhlakanipheni okuphakeme kuka-Euler noGauss abazichaza njengezingaqondakali, izinombolo eziyinkimbinkimbi zibonisa indlela imibono engaqondakali engaholela ngayo ekusetshenzisweni okusebenzayo okujulile. Ngokuqonda imvelaphi yazo, siyakwazisa ukugxuma kusuka 'kokucabanga' kuya kokungavamile kokubili kumbono kanye nokusebenza.
