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Deg tusnakt, amḍan asemlal d amḍan yezmer ad yettwasumer s talɣa a + bi, anda (a) d (b) id sin n yimḍanen ilawen, ma d i d yiwet n tigget tasnumkant (d anamek-is ur nezmir ara ad tt-naf deg tilawt) yettwammlen akken i² = −1. Amḍan ( a ) yettwasemma d amur ilaw n umḍan asemlal, ma d ( b ) d amur asugnan-ines.
Tagrumma n yimḍanen isemlalen tettwasemma s uzemz C. Tesnulfa-d akken ad tesnerni tagrumma n yimḍanen ilaw R s umḍan i yesɛan tazmert ad yefk tifrat i kra n tenkarin ur nesɛi ara tifrat deg R, am x² = −1. Yal amḍan ilaw d amḍan asemlal anda amur asugnan-ines d ilem. Ihi, tagrumma n yimḍanen ilaw d tadugrumma n tegrumma n yimḍanen isemlalen.
Yella waṭas n yisnasen n yimḍanen isemlalen deg yiḥricen yemgaraden n tusnakt d tussna. Deg tsengama, ttusemrasen deg uselmed n wahilen n trisiti akked umussu ahuzzan. Deg tsengama tatrart, ttusemrasen deg tenfalit n yimrigen imaẓlayen. Deg tesnileswalt tanmettit, ttusemrasen deg uselmed n yiferdisen n tutlayt. Ttusemrasen daɣen deg uẓawan d uselmed n yiẓuran n tenkarin.
Amḍan i d tigget tasugnant. Yettwammel s i² = -1. Asekcam n umḍan-agi yefka tazmert i tusnakt ad taf tifrat i waṭas n tenkarin ur nesɛi ara tifrat deg umaɣrad n yimḍanen ilaw.
Amḍan asemlal z = a + bi yegber sin n yiḥricen:
Z = a + bi Anda:
Z = r(cos(ϕ) + i sin(ϕ)) Anda:
Tikwal amḍan asemlal yettwaru deg yiwet n talɣiwin igi:
azal amagdez n umḍan asemlal z d aẓar amkuẓ n timernit n yimkuẓen n yiḥricen ilawen akked isugnanen :
akken ad nsiḍen θ sef talɣa taljebrit a + bi, nezmer ad nessemres tiwuriwin arccos, arcsin neɣ arctan :
Ma yella d sin n yimḍanen isemlalen:
Timernit n sin yimḍanen isemlalen d timernit n yiḥricen ilawanen d yiḥricen isugnanen yal yiwen ɣer wayeḍ.
Ma yella d sin n yimḍanen isemlalen:
Afaris n sin yimḍanen isemlalen yettwaxdem s usemres n tsuddest s usmekti bell i
Ma yella d sin n yimḍanen isemlalen ():
Taẓunt n sin yimḍanen isemlalen tettwaxdem s usemres n uneftay n umḍan asemlal deg umetṭerf d wadda, sakin s ubeṭṭu n ufaris ɣef tigget.
Aneftay n umḍan asemlal id .
Aneftay yesɛa amur ilaw yecrek d umḍan amenzu, ma d amur asugnan yettuɣal d amgal-is.
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