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側偍丆忋偺僾儘僌儔儉偱丄$\sqrt{-1}$ 偲偼 -1 偺暯曽崻丆嫊悢扨埵 i 偲屇偽傟傞傕偺偱偡偑丄
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惓幃偺島墘撪梕僪僉儏儊儞僩偼pdf宍幃偺傕偺傪尒偰壓偝偄丏
埲壓偺傕偺偼丆巆擮側偑傜丆HP偵嵹偣傞偺偑崲擄側婰崋側偳傪徣棯偟偰偍傝傑偡偺偱丆
偁偔傑偱奣棯偱偁傝傑偡丏
偳偆偐偛椆彸壓偝偄丏
偙偙偱偄偆寢傃栚偲偼丄恾侾(figure1)偺傛偆偵暵偠偨乮偮傑傝 "抂偑柍偄" 偲尵偆偙偲偱偡乯昍偺偙偲偱偡丅
偙偺傛偆側昍偼丄嬻娫偺拞偱愗偭偨傝偮側偄偩傝偟側偄偱丄偄傠偄傠側宍偵摦偐偡偙偲偑偱偒傑偡偑丄
偙偺傛偆側曄宍偱偆偮傝偁偆寢傃栚偼 "摨偠傕偺" 乮悢妛偺梡岅偱偼 "摨抣" 偲偄偄傑偡乯偲峫偊傞
偙偲偵偟傑偡丅乮摿偵恾俀(figure 2)偺條偵慡偔寢偽傟偰偄側偄寢傃栚偺偙偲傪丄 帺柧側"寢傃栚" 偲屇傃傑偡丅乯
偄傑 "擇偮偺寢傃栚偺奊偑梌偊傜傟偨偲偒丄偦傟傜偑摨偠寢傃栚傪昞偡偐偳偆偐敾掕偡傞" ol偲偄偆
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偲偙傠偑偁傟偽岾偄偱偡丅
嶳岥 |
"悢'' $\sqrt{-1}$ 偲偺巹偺椃 |
仠晛捠偺悢 x 偼乮偦傟偑 0 偱側偄偐偓傝乯
3^2=3 * 3 = 9 >0, (-3)^2 = (-3) * (-3) = 9 >0
偺傛偆偵丄忢偵暯曽偡傞偲惓偺悢偵側傝傑偡丗
x^2=x * x >0\;.
偲偙傠偱丄恖椶偼侾俇悽婭弶摢偵
仜^2 = -1
偲側傞 "悢''仜傪峫偊弌偟傑偟偨丅偙傟傪
\sqrt{-1} 傑偨偼 i
偲彂偒丄乽嫊悢扨埵乿偲尵偄傑偡丅乮拲乯
偙偺島墘偱偼丄偙偺嫊悢 i 偑寛偟偰 "嫊'' 偺悢偱偼側偔偰丄旕忢偵桳梡側丄旤偟偄悢偱偁傞
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乮拲乯 i 偼侾俉悽婭偺僗僀僗惗傑傟偺悢妛幰 Euler乮僆僀儔乕乯偑摫擖偟偨婰崋丅
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(1) 乽myxqbkdevkdsyxc yx iyeb cemmocc乿
(2) 乽lvsxefknmfkdvsh vs zvne hnllrhh乿
偙傟偺尨暥乮暯暥乯偼丄摨堦偺塸暥偱偡丅俀俇暥帤偺傾儖僼傽儀僢僩偺傒梡偄偰偄傑偡丅
(1) 偼乽僔乕僓乕宆埫崋乿傕偟偔偼乽僔僼僩埫崋乿偲屇偽傟傞傕偺偱丄
(2) 偼偦傟傪奼挘偟偨乽傾僼傽僀儞宆埫崋乿偲屇偽傟傞傕偺偱偡丅
Hint
夝撉乽惉岟乿傪廽偟偰丄慜傕偭偰乽偍傔偱偲偆乿偲弎傋偰偍偒傑偟傚偆丅
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