Ukuqonda iNgcebiso ka-'i' kwiMathematika
Hayi, ihlabathi lamanani entelekelelo! Kufana nokuzama ukucacisa ikhowudi eyimfihlo enengqiqo kodwa engaqondakaliyo kwangaxeshanye. Masingene nzulu emngxunyeni wemivundla kwaye siphonononge ummandla we-whimsical ka-'i' kwimathematika.
Ukuqonda iNgcebiso ka-'i' kwiMathematika:
Ngoko ke, makhe sityhile intsonkotha eyimfihlakalo ka 'i'. Xa sithetha ngo-'i', asithethi ngawe, ndithetha ukuthi “wena”, kodwa ke eli nani lentelekelelo elishukumisa iiequations zezibalo. Khawube nomfanekiso woku: xa usikwere 'i', ijika ibe yimvukelo -1. Ewe, kufana nokubetha ijekhiphothi yezibalo – engalunganga!
Okona kumnandi kukuba 'i' ngu-√-1 - khawucinge nje ngegorha elicingayo elizifihle kumanani alindele ukukhululwa! Le yunithi yomlingo idlala indima ebalulekileyo ekuvezeni loo manani antsokothileyo antsokothileyo apho axuba ubunyani kunye nentelekelelo ethile enzulu.
Sinxibe iminqwazi yethu yabacuphi bezibalo, masiqhaqhe enye iphazili: kwenzeka ntoni xa u-cube 'i'? Kulungile, ilula – yicinge njengoko ndiphinda-phinda kabini enye i-sneaky i. Xa udlala malunga neziseko kunye nee-exponents ekuphindaphindeni, izinto ziqala ukuba nomdla. Ngoko ke, i-cubed ngokuyimfuneko iphindwe kabini ukuya kumandla okuqala - voila! Uzifumene i ukuya kumandla wesithathu.
Ngoku, nali icebiso langaphakathi elisuka ngqo kwiMath Land: Wakha wazibuza ukuba ungajongana njani namandla ka-'i'? Ngokwahlula amandla ngo-4 kwaye ufumane intsalela, unokutyhila ngokulula imo yokwenyani. Umzekelo, u-i3 ulingana no -i; ngenisa i-domain yamanani anzima!
Sukubila xa uthelekisa ii-apile neeorenji okanye zokwenyani kunye nexabiso lentelekelelo- kufana nokuthelekisa ii-hotdogs kunye neeunicorns; azixubani! Ngoko ke khumbula lo mgaqo wegolide: awukwazi ukuthelekisa u-'i' no-1 kuba enye iyinyani ngelixa umlinganiswa wethu oyintloko 'i' enebhongo engeyonyani…njengentsomi yezibalo engenamaphiko.
Njengoko sitsiba kulo mhlaba umangalisayo wezibalo uzaliswe ziiyunithi zentelekelelo kunye namandla azo, gcina ingqondo yakho ibukhali ukuze ufumane iipuzzle ezigoba ingqondo ezingaphambili. Hlala ubukele ukuze ufumane iihacks zezibalo ezingaqondakaliyo kwaye wamkele i-wizard yakho yezibalo yangaphakathi!
Masiqhubeke nokugrumba nzulu kumngxunya wethu wemivundla ozaliswe yinyani kwaye sibhaqe imimangaliso yezibalo esilindele kufutshane nekona...
Ukuphonononga aMandla kunye neepateni zika-'i'
Ukuphonononga aMandla kunye neepateni zika-'i':
Makhe singene kwihlabathi elinomdla lamanani entelekelelo kwaye sityhile iimfihlo ezifihliweyo ngaphakathi kwamandla ka-'i'. Ipatheni yala magunya ifana nomdaniso ohlekisayo – ingumjikelo, uphinda-phinda zonke ii-exponents ezi-4. Xa i-exponent iphindwa ngo-4, ubetha i-jackpot ngesiphumo sika-1. Ukuba yinto enye kunophinda-phindwa ka-4, ufumana 'i', kwaye ipateni iyaqhubeka kwesi singqisho esiyimfihlakalo.
Ngoku, makhe sithethe ngomthetho ongaqondakaliyo othi 'i squared'. Ziqinise ngesi sityhilelo sigoba ingqondo: u-i ophindwe kabini (i^2) ulingana no -1. Kufana nokujika imathematika entloko – kaloku, phantse ngokoqobo! Yiba nomfanekiso-ngqondweni uthatha u-'i', uyigqabhuze, kwaye uphele nge-ego yayo enemvukelo, -1.
Kodwa khawume – kukho okungakumbi kulo mboniso womlingo wezibalo! Kwenzeka ntoni xa sibeka 'i'? Ewe, i cubed (i^3) isinika -i. Yimathematika ukuba ezi nxaki zidlala njani njengephazili elindele ukusonjululwa.
Njengoko singena ngakumbi kuhambo lwethu lwamanani, masingalibali malunga ne-i kumandla ka-1. Igubu eliqengqelekayo nceda… Amandla e-i yakhululwa asinika – uqikelele ukuba kulungile – ndimdala kakuhle 'i'. Kwaye xa siyinyusela kumagunya aphezulu silandela ipateni yethu emangalisayo yebhayisikile nganye kwii-exponents ezi-4, sityhila i-symphony ekwimo yezibalo.
Wakhe wacinga ukuba ingcambu ka-1 ingaba ngu 'i'? Kwizifundo zemathematika, √(-1) usebenzisa amandla amakhulu phantsi kwesimboli 'i' njengenxalenye yethu yentelekelelo ethandwayo yamaqhawe eequation zamanani. Kodwa kulwimi lwe-elektroniki, apho ulawulo lwangoku luphezulu kusetyenziswa u-'i', ngena eqongeni ushiye umzala wakhe 'j' njengophawu olujikelezayo kunye nemisinga yombane.
Ngamandla kunye nepateni nganye etyhilwe kule saga yamanani, khumbula ukuba imathematika inokusimangalisa ngalo lonke ixesha ngamakhubalo ayo entelekelelo kunye nemithetho ecela ukuba ityhilwe. Ke bopha iiseli zakho zobuchopho njengoko sijija kwaye sijika kulo mhlaba umangalisayo apho inyani idibana nokucinga ngemvisiswano yedijithali egqibeleleyo!
Indima yamanani aqikelelwayo kwizibalo ezintsonkothileyo
Kwizibalo ezintsonkothileyo, amanani entelekelelo adlala indima ebalulekileyo njengoko ekhulisa ummandla wezisombululo ngaphaya kwamanani okwenene. Ingqikelelo ethi 'i ophindwe kabini ilingana -1' isisiseko kwihlabathi lamanani antsokothileyo, apho u-'i' emele iyunithi yentelekelelo. Ngokuchaza u-i njengo-√-1, sazisa umgangatho omtsha kwimathematika apho ukuphindaphinda u-'i' ngokwako kukhokelela kwixabiso elibi. Le propati ivula ihlabathi lamathuba ekusombululeni ii-equations ezingenazo izisombululo zenani lokwenyani.
Xa isiza ekuqondeni ixabiso lika-i ophindwe kabini kumanani entelekelelo, kubalulekile ukuqonda ukuba inani lentelekelelo yimveliso yenani lokwenyani kunye neyunithi yentelekelelo 'i'. Isikwere senani lentelekelelo elifana no-bi ngu-b2. Umzekelo, ukuba sithatha u-5i njengenani lentelekelelo, isikwere salo siya kuba ngu -25. Olu balo lubonisa ukuba i-squaring kwi-imaginary number ivelisa njani isiphumo esibi, iqaqambisa indlela eyodwa yokuziphatha kwezi ziko zinzima.
Isizathu emva kwe-i2 yokulinganisa -1 ilele kwimeko eyahlukileyo yamanani entelekelelo. Ngokungafaniyo namanani okwenyani anezikwere ezisoloko zi-non-negative, xa singena kwindawo yamanani antsokothileyo ngo-'i', izinto ziba nomdla. Ingcambu ka -1 ayikho phakathi kwamanani okwenyani esintu kodwa iyasazisa kweli qumrhu lomlingo libizwa ngokuba ngu'i'. Ngaloo ndlela, i-i2 ilingana no -1 ibonisa indlela imathematika enokuyigoba ngayo imigaqo yayo kwaye isimangalise ngokuntsokotha kwayo okunamandla.
Ngapha koko, unxibelelwano phakathi kwenombolo enzima u-i kunye no-1 luvela xa ujongana namaxabiso angalunganga ngaphakathi kweengcambu zamanani anzima. Apha kulapho 'i' angena khona ukumela leyunithi yomlingo esisikwere esisombulule ngomlingo ukuya ku -1. Olu bhalo lufuziselayo olufana no-'i' okanye ngamanye amaxesha no-'j' lunika iingcali zezibalo izixhobo ezicacileyo ezizifunayo xa zijonga iiequation ezintsonkothileyo ezifuna izisombululo ezingaphaya kwamanani okwenyani aqhelekileyo.
Ke kwixesha elizayo xa udibana ne-i2 = -1 kwimibuzo yakho yemathematika, khumbula ukuba le mithetho inzima yiyo eyenza ukuba imathematika ibe nomdla kwaye ibemnandi kakhulu- njengokutyhila iphazili apho inyaniso idibana nokucinga ngokuvisisana ngokugqibeleleyo!
Yintoni ixabiso lika-i?
Ixabiso lika-i ngu-√-1.
Yintoni i cubed ilingana kwizibalo?
i cubed ilingana no -i.
Ngaba ndimncinci kuno-1?
Awunakuthelekisa phakathi kwamaxabiso amabini angeyonyani okanye phakathi kwexabiso lokwenyani nelingelokwenyani. Ngoko ke, awukwazi ukuthelekisa u-i kunye no-1 kuba i ingeyonyani ngelixa u-1 eyinyani. Ekuphela kwento onokuyithelekisa ngamaxabiso azo apheleleyo.
Uyisombulula njani kumandla we-i?
Ukusombulula kumandla we-i, ungasebenzisa indlela yokwahlula amandla ngo-4 ukufumana intsalela. Umzekelo, u-i3 ulingana -i ngamanani antsokothileyo.