1.1 Definicion y Origen de Los Numeros Complejos

 

\BEIHI 8 BßALWDZ JDASNLODZ 8.8  Il`ebejeúb y Dreklb il nds bÿalrds jdapnlods

\bh jhbteihi eahkebhreh bd ls aès qul nhs rhájls ebiejhihs phrls ∗8, ∟ ∗:, ∗:, ∟ ∗= ∗= sdb jhbteihils eahkebhrehs. phrh jhbteihils blkhtevhs. Hsá ∟ ∗8, ∗8 ls nnhahih „ubeihi eahkebhreh‑ , hsá, nh ubeihi Nh jhbteihi eahkebhreh ∟ ∗8 ∗8 . Lb lnljtrejeihi   sl ilbdth jdad eahkebhreh sl ilbdth jdad  ∹  1 ∟ ∗8  . \b bÿalrd jdapnlod telbl nh `drah  1  +  , lb idbil h y g sdb bÿalrds rlhnls l   ls ub sáagdnd jdb prdpelihi il qul  7 1 ∗8, pdrqul ∗8 Û ∟ ∗ 8 1 ∗ 8. Ln bÿalrd  ls nh phrtl rlhn il , ilbdthih jdad    y ∟ ∗8  ls nh phrtl eahkebhreh il , ilbdthih jdad   . Zl jdbseilrh qul ids bÿalrds jdapnlods sdb ekuhnls se, y sdnd se, sus phrtls rlhn l eahkebhreh ( + )  sdb ekuhnls se sus phrtls rlhnls sdb sdb ekuhnls. Hsá, ( +  )  ( ekuhnls y sus phrtls eahkebhrehs sdb ekuhnls6 lstd ls, se  1    1  . Zl jdbseilrh qul ub bÿalrd rlhn h ls ub tepd lspljehn il bualrd jdapnlod, hn eilbte`ejhr  jdb  + 3 . Aès hÿb, nhs dplrhjedbls hretaåtejhs jdb bÿalrds rlhnls pulilb hapnehrsl hn jdboubtd il nds bÿalrds jdapnlods. Ln sestlah il bÿalrds jdapnlods, ilbdthid aliehbtl j, ls ln jdboubtd il tdids nds bÿalrds jdapnlods. Nds bÿalrds jdapnlods hphrljlb hn trhthr trh thr il rlsdnvlr ljuhjedbls iln tepd  7 + 8 1 3. Ilsplohbid h  sl dgtelbl  1 ∟ ∗8 ∗8 ,  qul sl lsjregl  1  .  Ln dreklb il nds bÿalrds jdapnlods sl rladbth hn seknd ]PE lb qul Jhrihbd nnhaú rház `ejtejeh h nhs rhájls blkhtevhs il ubh ljuhjeúb. Dtrds ahtlaètejds pdstlredralbtl nhs nnhahrdb rhájls `hnshs d rhájls sdrihs. Lb 8