ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠋ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢ ᠥᠷᠭᠡᠵᠢᠯᠦᠯᠵᠦ᠂ $ x^{2}+1=0 $ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠢ ᠰᠢᠢᠳᠦᠯ ᠲᠡᠢ ᠪᠣᠯᠭᠠᠭᠰᠠᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠶᠤᠮ᠃
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠢᠢ a + bi ᠬᠡᠯᠪᠡᠷᠢ ᠪᠡᠷ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠡ ᠡᠭᠦᠨ ᠳᠦ ᠨᠢ a ᠪᠣᠯᠤᠨ b ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋᠂ i ᠨᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠪᠢᠭᠡᠳ i2 = −1 ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠢᠢᠳᠦᠯ ᠢ ᠬᠠᠩᠭᠤᠭᠰᠠᠨ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
ᠳᠦᠷᠡᠰᠦᠯᠡᠯ
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠨᠢ ᠬᠡᠪᠲᠡᠭᠡ ᠲᠡᠩᠬᠡᠯᠭᠡ ᠪᠠ ᠪᠣᠰᠤᠭ ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠭᠡ ᠡᠴᠡ ᠪᠦᠷᠢᠳᠦᠳᠡᠭ᠃
ᠬᠠᠭᠤᠷᠮᠠᠬ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠰᠤᠭ ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠭᠡ ᠳ᠋ᠦ ᠪᠠᠢᠢᠷᠢᠰᠢᠳᠠᠭ᠃
ᠬᠡᠪᠲᠡᠭᠡ ᠲᠡᠩᠬᠡᠯᠭᠡ ᠳ᠋ᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠭᠤᠯᠳᠠᠭ᠃
ᠦᠢᠯᠡᠳᠦᠯ
ᠨᠡᠮᠡᠬᠦ
ᠬᠣᠶᠠᠷ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠨᠡᠮᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠵᠦ᠂ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠨ ᠡ᠋᠃[1]
$ (a+bi)+(c+di)= $ $ =(a+c)+(b+d)i $
ᠬᠠᠰᠤᠬᠤ
ᠨᠢᠭᠡ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠡᠴᠡ ᠨᠥᠭᠦᠳᠡ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠰᠠᠬᠤ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠪᠠ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ᠦᠳ ᠢ ᠲᠤᠰ ᠪᠦᠷᠢ ᠬᠠᠰᠤᠶᠤ᠃[1]
$ (a+bi)-(c+di)= $ $ =(a-c)+(b-d)i $
ᠦᠷᠡᠵᠢᠬᠦ
ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ᠦᠨ ᠰᠡᠯᠭᠦᠬᠦ (commutative)᠂ ᠪᠦᠯᠦᠭᠯᠡᠬᠦ (associatove)᠂ ᠵᠠᠳᠠᠯᠬᠤ (distributive) ᠴᠢᠨᠠᠷ ᠤᠳ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ ᠃[2]
$ (a+bi)(c+di)= $ $ =ac+bci-bd+adi= $ $ =(ac-bd)+(bc+ad)i $
ᠬᠤᠪᠢᠶᠠᠬᠤ
ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠳᠤ ᠦᠢᠯᠡᠳᠦᠯ ᠭᠦᠢᠴᠡᠳᠬᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠬᠤᠪᠢᠶᠠᠭᠴᠢ ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ᠲᠣᠭᠠ᠋ ᠢᠢ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃ ᠬᠤᠪᠢᠶᠠᠷᠢ ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ᠢᠢᠠᠷ ᠬᠦᠷᠲᠡᠪᠦᠷᠢ ᠪᠠ ᠬᠤᠪᠢᠶᠠᠷᠢ ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠳᠡᠭ᠃
$ {\frac {a+bi}{c+di}}= $
$ ={\frac {\left(a+bi\right)\left(c-di\right)}{\left(c+di\right)\left(c-di\right)}}= $
$ ={\frac {ac+bd}{c^{2}+d^{2}}}+\left({\frac {bc-ad}{c^{2}+d^{2}}}\right)i. $
- ↑ Jump up to: 1.0 1.1 ᠰᠡᠷᠳᠠᠮᠪᠠ ᠪᠥᠬᠡᠪᠠᠲᠤ᠃ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠ᠃ Geogebra. https://www.geogebra.org/m/CwryWtd9?fbclid=IwAR0i1VN-HH5hegFJoWMjgCM9si7zH7x9hHDuEbU6iROuW3gbqIAeMGngvAs#material/nLiRDrsU ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/08/17
- ↑ Виленкин Н. Я., Ивашов-Мусатов О. С., Шварцбурд С. И. Алгебра и математический анализ для 11 класса. Учебное пособие. — Изд. 6-е. — М.: Просвещение, 1998. — 288 с. — ISBN 5-09-008036-4.