Complex nhamba. Kukosha uye Evolution "zvekufungidzira tsika"

The nhamba - inokosha kwemasvomhu zvinhu zvinodiwa kuti zvakasiyana computations uye Masvomhu. Yakatarwa dzinongoitika, integer, musoro uye musoro digitaalinen tsika rinotsanangura muzvizhinji kunzi chaizvo nhamba. Asi panewo muchikwata zvikuru kujairika - ". Zvekufungidzira zvakawanda" dzakaoma nhamba kunorondedzerwa René Descartes se Uye mumwe vaitungamirira mathematicians ari namasere remakore Leonhard Euler zvinganaka kunan'anura kwavari tsamba Ini kubva French shoko imaginare (zvekufungidzira). Ndeipi dzakaoma nhamba?

Saka akadana zvinoratidza chimiro + bi, uko, uye, b ndezvechokwadi nhamba, uye ini digital chokukomborerwa dzinokosha ane mativi ari -1. Operations ari kunzwisisa nhamba anoitwa chete mitemo sezvo siyana kwemasvomhu mashandiro ari polynomials. chikamu ichi kwemasvomhu harumiririri migumisiro ipi kuyerwa kana Masvomhu. Nokuti izvi inokwana chaiyo nhamba. Sei, zvino, vachifanira?

Complex nhamba somunhu kwemasvomhu pfungwa, zvakakodzera nokuti kuti vamwe equations vane chaiko coefficients vane zvinogadzirisa mumunda nhamba "zvavo". Saka, kuwedzera kukura kwebasa kugadzirisa Misiyano vakasimuka kudiwa kusuma mhando itsva akarongeka. Complex nhamba vane kunyanya yokungotaura tiivistelmä zvibvire kugadzirisa equations izvi sezvo ² x 1 = 0. It rinozivikanwa kuti, pasinei ayo pachena chirango ichi chikamu nhamba zvinoshingaira uye zvikuru kushandiswa, semuenzaniso, nokuti zvakasiyana mazano anoshanda zvinetso elasticity dzidziso, zvemagetsi engineering, aerodynamics uye hydromechanics, mabhomba wefizikisi nezvimwe anoranga yesayenzi.

Module uye nharo ane kunzwisisa nhamba wakashandiswa pakuvaka purogiramu. chimiro ichi kunyora inonzi trigonometric. Uyezve, mashoko geometrical kududzira nhamba ano mberi akawedzera kutsanangurwa chikumbiro chavo. Zvakakwanisika kuzvishandisa kuti dzakasiyana-siyana kadambari mepu.

Masvomhu yasvika kure mano dzinongoitika nhamba kuti zvakaoma Integrated gadziriro dzavo mabasa. Nezvenyaya iyi vanogona kunyora yoga Tutorial. Pano tinotarisa dzimwe shanduka zvinhu zviri nhamba dzidziso, pachena ose nhoroondo uye masayendisiti mamiriro pfungwa pamusoro muchikwata ichi akarongeka.

Yemasvomhu vaiona "wechokwadi" chete zvakasikwa nhamba, izvo zvinogona kushandiswa exchange chinhu. Nechekare mumireniyamu yechipiri BC. e. vaEgipita vekare uye nevaBhabhironi muna zvakasiyana dzinoshanda Masvomhu nokushingaira vaishandisa zvikamu zviduku. Chinotevera rinokosha kukosha kukura wemasvomhu kwaiva kuonekwa kunaka nhamba China rekare makore mazana maviri asati munhambo yedu. Vakanga zvakashandiswawo vekare yemasvomhu Diophantus, vaiziva mitemo mano amabasa pamusoro pavo. Achibatsirwa kunaka nhamba, zvakakwanisika kurondedzera kuchinja siyana mune tsika, kwete chete akanaka ndege.

Muzana remakore rechinomwe AD, zvakanga zvakajeka yakasimbiswa kuti mativi midzi yakanaka nhamba dzose dzine tsika mbiri - mukuwedzera zvakanaka, uyewo kunaka. Kubva yokupedzisira dzokubvisa yaiungana pamudzi zvatinosiita algebraic nzira iyoyo zvaifungwa hazviiti: hakuna ukoshi kwakadaro X kuti X ² = ─ 9. Nokuti havana basa nguva refu. Yakanga chete nenhanhatu remakore, apo paiva uye vave achishingaira vadzidza cubic equations, kudiwa dzokubvisa mativi mudzi yakaipa nhamba, sezvo iri nzira yokuti agadzirise mashoko aya rine kwete chete kuutio, asiwo mativi midzi.

fomura Izvi akasimba, kana kuti mukana wokuti vanhu vanga ane dzakawanda imwe mudzi chaiwo. Kana kuvapo muna mukana wokuti vanhu vanga matatu zvechokwadi midzi kuti mushonga wavo rwaiwanikwa nokuwanda kunaka ukoshi. Zvakaratidza kuti inoenda apore anomhanya kuburikidza matatu midzi zvisingabviri mumaonero samhu oparesheni nguva.

Kuti utsanangurirwe kunoguma gangaidzo Italian algebraists J. Cardano akanga aronga kuti ataure muchikwata itsva kujairika zvakaita nhamba, makatumidzwa yakaoma. Handizive kuti iye Cardano akaona asingabatsiri uye akaita zvose kudzivisa kushandisa kuti yaida kwemasvomhu mhando. Asi kare muna 1572 rimwe bhuku kwakaonekwa chimwe algebraist Italian Bombelli, zvakanga zvakawanda mitemo mabasa ari dzakaoma nhamba.

Mumazana nemanomwe remakore akaramba pokukurukurwa kwemasvomhu yezvakaita date nhamba uye zvinogonekwa dzavo geometric dudziro. Also yakatanga zvishoma nezvishoma uye nani unyanzvi yokushanda navo. Uye kwezana remakore rechi17 nerechi18, mukuru dzidziso dzakaoma kunzwisisa nhamba akasikwa. An mupiro kukuru kuti kukura uye kuvandudzika pamusoro dzidziso mashandiro anoita variables kunzwisisa wakatangwa Russian uye masayendisiti neSoviet. N. I. Muskhelishvili mubasa rayo chikumbiro matambudziko dzidziso elasticity, Keldysh uye Lavrentiev kunzwisisa nhamba zvave mumunda hydro- uye aerodynamics, uye Vladimir Bogolyubov - mune quantum munda dzidziso.