"ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ"-ны өөр хувилбарууд
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|<span style="writing-mode: horizontal-tb;"> i<sup>0</sup>=1 | |<span style="writing-mode: horizontal-tb;"> i<sup>0</sup>=1 | ||
|<span style="writing-mode: horizontal-tb;"> =i | |<span style="writing-mode: horizontal-tb;"> i<sup>1</sup>=i | ||
|<span style="writing-mode: horizontal-tb;"> =-1 | |<span style="writing-mode: horizontal-tb;"> i<sup>2</sup>=-1 | ||
|<span style="writing-mode: horizontal-tb;"> =-i | |<span style="writing-mode: horizontal-tb;"> i<sup>3</sup>= i<sup>2</sup> • i = (-1) • i=-i | ||
|- | |- | ||
|<span style="writing-mode: horizontal-tb;"> i<sup>4</sup>=1 | |<span style="writing-mode: horizontal-tb;"> i<sup>4</sup> = i3 • i = (-i) • i = -i2=1 | ||
|<span style="writing-mode: horizontal-tb;"> =i | |<span style="writing-mode: horizontal-tb;"> i<sup>5</sup>= i 4• i = 1 • (i) =i | ||
|<span style="writing-mode: horizontal-tb;"> =-1 | |<span style="writing-mode: horizontal-tb;"> i<sup>6</sup> i 4• i2 = 1 • (-1) =-1 | ||
|<span style="writing-mode: horizontal-tb;"> =-i | |<span style="writing-mode: horizontal-tb;"> i<sup>7</sup>= i 4• i3 = 1 • (-i) =-i | ||
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|<span style="writing-mode: horizontal-tb;"> i<sup>8</sup>=1 | |<span style="writing-mode: horizontal-tb;"> i<sup>8</sup>= i 4• i4 = 1 • 1=1 | ||
|<span style="writing-mode: horizontal-tb;"> =i | |<span style="writing-mode: horizontal-tb;"> i<sup>9</sup>= i 4• i 4• i = 1 • 1• i=i | ||
|<span style="writing-mode: horizontal-tb;"> =-1 | |<span style="writing-mode: horizontal-tb;"> i<sup>10</sup>= (i 4)2 • i2 = 1 • (-1) =-1 | ||
|<span style="writing-mode: horizontal-tb;"> =-i | |<span style="writing-mode: horizontal-tb;"> i<sup>11</sup>= (i 4)2 • i3 = 1 • (-i)=-i | ||
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23:21, 3 Долоодугаар сар 2021-ий байдлаарх засвар
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠪᠣᠯ ᠥᠪᠡᠷ ᠲᠦ ᠢᠨᠦ ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ -1 ᠭᠠᠷᠳᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠶᠤᠮ᠃
ᠥᠭᠡᠷ ᠡ᠋ ᠪᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠻᠸᠠᠲᠷᠠᠲ᠋ ᠵᠡᠷᠭᠡ ᠢᠨᠦ -1 ᠤᠳᠬ ᠠ᠋ ᠠᠪᠳᠠᠭ (i2 = -1) ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠭᠡᠨ ᠡ᠋᠃
ᠪᠠᠰᠠ -1 ᠢᠢᠨ ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ ᠠᠨᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠭᠡᠵᠦ ᠬᠡᠯᠡᠵᠦ ᠪᠣᠯᠤᠨ ᠠ᠋:
ᠠᠩᠭᠯᠢ ᠪᠠᠷ imaginary unit, ᠣᠷᠤᠰ ᠢᠢᠠᠷ мнимая единица ᠬᠡᠮᠡᠬᠦ ᠡᠨᠡ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ ᠠᠨᠤ ᠲᠥᠰᠦᠭᠡᠯᠡᠯ ᠨᠢᠭᠡᠴᠡ᠂ ᠲᠥᠰᠦᠭᠡᠯᠡᠭᠰᠡᠨ ᠨᠢᠭᠡᠴᠡ᠂ ᠬᠣᠭᠤᠰᠤᠨ ᠨᠢᠭᠡᠴᠡ᠂ ᠬᠡᠢᠢᠰᠪᠦᠷᠢ ᠨᠢᠭᠡᠴᠡ ᠭᠡᠰᠡᠨ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ᠃
ᠬᠠᠯᠨᠮᠠᠭ ᠲᠦᠮᠡᠨ imaginary number ᠬᠡᠮᠡᠬᠦᠢ ᠢᠢ ухалдаг тойг (ᠤᠬᠠᠭᠠᠯᠠᠳᠠᠭ ᠲᠣᠭᠠ) ᠬᠡᠮᠡᠨ ᠪᠠᠭᠤᠯᠭᠠᠭᠰᠠᠨ ᠪᠠᠢᠢᠬᠤ ᠲᠤᠯᠠ imaginary unit ᠭᠡᠳᠡᠭ ᠢ ᠪᠠᠰᠠ "ᠤᠬᠠᠭᠠᠯᠠᠳᠠᠭ ᠨᠢᠭᠡᠴᠡ" ᠭᠡᠵᠦ ᠪᠠᠭᠤᠯᠭᠠᠳᠠᠭ ᠪᠤᠢ ᠵᠠ᠃
ᠨᠥᠭᠦᠭᠡᠲᠡᠭᠦᠷ᠂ ᠪᠤᠶᠤ ᠬᠠᠰᠠᠬᠤ ᠨᠢᠭᠡ ᠢᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠰᠢᠢᠳᠦᠯ ᠢᠨᠦ i ᠲᠡᠳᠦᠢ ᠦᠭᠡᠢ ᠪᠠᠰᠠ -i ᠪᠠᠢᠢᠬᠤ ᠶᠤᠮ᠃[1]
ᠬᠠᠷᠢᠨ комплексное число ᠭᠡᠳᠡᠭ ᠢ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷᠡ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠬᠠᠪᠰᠤᠷᠠᠭᠰᠠ ᠲᠣᠭᠠ" (ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰcomplex ᠲᠣᠭᠠ) ᠬᠡᠮᠡᠵᠦᠬᠦᠢ᠃[2]
ᠵᠠᠷᠢᠮ ᠦᠢᠯᠡᠳᠦᠯ
ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠷᠴᠡ ᠪᠤᠶᠤ i ᠲᠣᠭᠠᠨ ᠳ᠋ᠦ ᠦᠷᠵᠢᠬᠦᠯᠦᠭᠰᠡᠨ ᠢᠢᠡᠷ᠄
ᠭᠠᠷᠤᠮᠤᠢ᠃
ᠡᠨᠡ ᠨᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠸᠧᠺᠲ᠋ᠣᠷ ᠢvector ᠨᠠᠷᠠ ᠪᠤᠷᠤᠭᠤ 90°ᠡᠷᠭᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠲᠡᠢ ᠠᠭᠠᠷ ᠨᠢᠭᠡᠨ ᠪᠤᠶ ᠠ᠋᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠳ᠋ᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ ᠨᠢ i ᠲᠣᠭᠠᠨ ᠤ ᠤᠷᠪᠠᠭᠤ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠲᠡᠢ ᠭᠠᠷ ᠨᠢᠭᠡᠨ:
ᠡᠭᠦᠨ ᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠬᠡᠷᠡᠭᠯᠡᠪᠡᠰᠦ:
ᠡᠨᠡ ᠨᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠸᠧᠺᠲ᠋ᠣᠷ ᠢvector ᠨᠠᠷᠠ ᠵᠥᠪ 90°ᠡᠷᠭᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠲᠡᠢ ᠠᠭᠠᠷ ᠨᠢᠭᠡᠨ ᠪᠤᠶ ᠠ᠋᠃
ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ
ᠲᠣᠭᠠ ᠢᠢ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠨᠢ ᠮᠥᠴᠢᠯᠭᠡ ᠪᠡᠷ ᠳᠠᠪᠲᠠᠭᠳᠠᠬᠤ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠲᠠᠢ᠃
i0=1 | i1=i | i2=-1 | i3= i2 • i = (-1) • i=-i |
i4 = i3 • i = (-i) • i = -i2=1 | i5= i 4• i = 1 • (i) =i | i6 i 4• i2 = 1 • (-1) =-1 | i7= i 4• i3 = 1 • (-i) =-i |
i8= i 4• i4 = 1 • 1=1 | i9= i 4• i 4• i = 1 • 1• i=i | i10= (i 4)2 • i2 = 1 • (-1) =-1 | i11= (i 4)2 • i3 = 1 • (-i)=-i |
ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ
- ↑ James Tamton. Encyclopedia of Mathematics. Facts on File Inc. New York 2005. ISBN 0-8160-5124-0
- ↑ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ᠃ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠮᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ᠃ ᠪᠦ᠊᠂ ᠨᠠ᠊᠂ ᠮᠣ᠊᠂ ᠠ᠊᠂ ᠤ᠊᠂ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠬᠡᠯᠡ ᠵᠣᠬᠢᠶᠠᠯ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ ᠤᠯᠤᠰ ᠤᠨ ᠬᠡᠪᠯᠡᠯ ᠦᠨ ᠬᠡᠷᠡᠭ ᠡᠷᠬᠢᠯᠡᠬᠦ ᠬᠣᠷᠢᠶ ᠠ᠋᠃ ᠤᠯᠠᠭᠠᠨᠪᠠᠭᠠᠲᠤᠷ 1964᠃