Complex lambobi. Darajar da Juyin Halitta "hasashen dabi'u"

The lambobin - ainihin ilmin lissafi abubuwa da ake bukata domin daban-daban computations da lissafin. A sa na halitta, lamba, m da m dijital dabi'u ma'anar da jam'i da ake kira real lambobi. Amma akwai kuma quite sabon abu category - hadaddun lambobin tsare ta Rene Descartes matsayin "hasashen yawa." Kuma daya daga cikin manyan lissafi na karni na sha takwas Leonhard Euler samarwa designate su da wasika i daga Faransa kalma imaginare (hasashe). Mene ne hadaddun lambobin?

Don haka ya kira maganganu na form wani + guda biyu, inda a kuma b ne real lambobi, da kuma i ne mai dijital nuna alama na musamman da darajar wanda square ne -1. Ayyuka a hadaddun lambobin an yi da wannan dokoki a matsayin daban-daban ilmin lissafi aiki a kan polynomials. Wannan ilmin lissafi category ba ya wakiltar da sakamakon wani ma'aunai ko lissafin. Domin wannan shi ne quite isa real lambobi. To, don me ba su bukatar?

Complex lambobin matsayin ilmin lissafi ra'ayi, dole saboda gaskiyar cewa wasu lissafai tare da real coefficients da mafita a cikin filin na "talakawa" lambobi. Saboda haka, domin fadada na warware daidaituwar tashi da bukatar gabatar da sabon ilmin lissafi Categories. Complex lambobin da ciwon yafi msar tambayar m zai yiwu a warware wadannan lissafai kamar yadda ² x 1 = 0. An lura da cewa, duk da bayyana ƙa'ida wannan category lambobin rayayye kuma yadu amfani, misali, ga daban-daban m mafita matsaloli na elasticity ka'idar, lantarki injiniya, aerodynamics da hydromechanics, atomic kimiyyar lissafi da kuma sauran kimiyya tarbiyya.

Module da shawara na wani hadadden yawan amfani a cikin shiri jadawalai. Wannan nau'i na rubuce-rubuce da kira trigonometric. Bugu da kari, da geometrical fassarar wadannan lambobi ya kara fadada ikon yinsa, na da aikace-aikace. Sai ya zama zai yiwu a yi amfani da su domin dama sarrafa kwamfuta taswira.

LISSAFI ya zo dogon hanya daga sauki halitta lambobi zuwa hadaddun Hadakar tsarin da su ayyuka. A kan wannan batu zai iya rubuta wani raba koyawa. Ga muka dubi kawai wasu daga cikin masana juyin halitta al'amurran da lambar ka'idar, bayyana shi duk da tarihi da kuma kimiyya bango ma'ana da wannan ilmin lissafi category.

Greek lissafi dauke "gaskiya" kawai halitta lambobi, wanda za a iya amfani da yin lissafi da wani abu. Tuni a cikin na biyu Millennium BC. e. zamanin d Masarawa, da Kaldiyawa a da dama m lissafin rayayye amfani kasarun adadi. A gaba muhimmanci milestone a cikin ci gaban ilmin lissafi ya bayyanar korau lambobin a zamanin d China shekara ɗari biyu kafin mu zamanin. Su ma an yi amfani da zamanin d Girkanci lissafi Diophantus, suka san dokokin sauki aiki a kan su. Da taimakon korau lambobin, ya zama zai yiwu don bayyana daban-daban canje-canje a cikin dabi'u, ba kawai a cikin m jirgin sama.

A cikin ƙarni na bakwai AD, an fili tabbatar da cewa square tushen tabbatacce lambobi ko da yaushe suna da biyu dabi'u - ban da kyau, kuma korau. Daga karshen cire square tushen na saba algebraic hanyoyin da cewa lokaci an yi tunanin zai yiwu ba: babu irin wannan darajar x zuwa x ² = ─ 9. Ga lokaci mai tsawo da shi bai hana kome ba. Shi ne kawai a cikin karni na sha shida, a lokacin da akwai kuma an rayayye karatu cubic lissafai, da bukatar cire da square tushen korau lambobi, kamar yadda a cikin dabara don bayani na wadannan maganganu ƙunshi ba kawai shigen sukari, amma kuma da square asalinsu.

Wannan dabara ne robust, idan lissafi yana a mafi daya real tushen. A cikin hali na gaban a lissafi na uku real Tushen su magani da aka samu tare da yawan mummunan darajar. Sai dai itace cewa hanya zuwa maida gudanar ta hanyar da uku tushen da ba zai yiwu ba daga mahangar lissafi na aiki lokaci.

Domin bayani game da sakamakon paradox Italian algebraists J. Cardano aka samarwa don gabatar da wani sabon category na sabon abu yanayin da lambobi, wanda ake kira hadaddun. Ina mamaki da abin da ya Cardano dauke su m, kuma suka aikata duk abin da ya gudana da ake ji da su zuwa ga samarwa ilmin lissafi Categories. Amma riga a 1572 a littafin bayyana wani Italian algebraist Bombelli, wanda suka cikakken dokoki domin gudanar a hadaddun lambobi.

Cikin goma sha bakwai karni ci gaba da tattaunawa da ilmin lissafi yanayin da data lambobi da kuma damar lissafi fassarar. Har ila yau, a hankali ɓullo da kuma inganta dabara na aiki tare da su. Kuma a nuna na 17th kuma 18th ƙarni, general ka'idar hadaddun lambobin da aka halitta. An babban taimako ga ci gaba da kuma kyautata na ka'idar ayyuka na hadaddun canji da aka gabatar Rasha da kuma Soviet masana kimiyya. N. I. Muskhelishvili tsunduma a aikace a cikin matsalolin da ka'idar elasticity, Keldysh da Lavrentiev hadaddun lambobin an yi amfani a fagen hydro- da aerodynamics, kuma Vladimir Bogolyubov - a jimla filin ka'idar.