ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠊ᠠ᠋
ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠢᠨᠦ ᠲᠡᠭ (0) ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠬᠠᠮᠠᠮᠦᠢ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠺᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠬᠠᠰᠤᠬᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠬᠠᠷᠢᠭᠤ ᠭᠠᠷᠤᠨ ᠠ᠋᠃[1]
ᠲᠡᠭᠡᠬᠦ ᠪᠡᠷ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠠᠭ ᠠ᠋ ᠠᠨᠤ ᠬᠠᠰᠤᠬᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠶ ᠲᠣᠭᠠᠨ ᠤ ᠬᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ ᠮᠥᠨ᠃
ᠲᠡᠭ (0) ᠲᠣᠭ ᠠ᠋ ᠪᠣᠳᠠᠲᠤ ᠪᠤᠶᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠠᠯᠢ ᠨᠢ ᠴᠤ ᠪᠠᠢᠢᠵᠤ ᠪᠣᠯᠤᠨ ᠠ᠋᠃
ᠳᠦᠷᠰᠦᠯᠡᠯ
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ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ ᠪᠦᠬᠦᠢ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠯ ᠤᠨ ᠳᠦᠷᠰᠦᠯᠡᠯ᠃ |
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᠃
ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠳ᠋ᠦ –1 ᠢᠢᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠰᠠᠨ 180 ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠤᠨ ᠠ᠋᠃
i ᠲᠣᠭ ᠠ᠋ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠯᠭᠦᠯᠬᠦ ᠢᠨᠦ ᠨᠠᠷᠠ ᠪᠤᠷᠤᠭᠤ “ᠡᠷᠡᠭᠦ” ᠴᠢᠭ᠌ ᠲᠦ 90 ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠬᠤ ᠪᠠ ᠬᠡᠷᠪᠡ i2 = -1 ᠭᠡᠰᠡᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠢᠨᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠰᠠᠨ 90 ᠬᠡᠮ ᠦᠨ ᠬᠣᠶᠠᠷ ᠡᠷᠭᠢᠯᠲᠡ ᠭᠡᠵᠦ ᠦᠵᠡᠪᠡᠯ ᠦᠷ ᠡ᠋ ᠳ᠋ᠦ᠋ᠩ ᠢᠨᠦ ᠭᠠᠭᠴᠠ 180 ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠤᠨ ᠠ᠋᠃
“ᠰᠥᠷᠭᠦ” (ᠨᠠᠷᠠ ᠵᠥᠪ) ᠴᠢᠭ᠌ ᠲᠦ 90 ᠬᠡᠮ ᠡᠷᠭᠢᠬᠦ ᠢᠨᠦ ᠮᠥᠨ ᠡᠨᠡ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠳ᠋ᠦ ᠨᠡᠶᠢᠴᠡᠬᠦ ᠪᠠ x2 = -1 ᠭᠡᠰᠡᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠶ᠋ᠢᠳ −i ᠪᠣᠯᠬᠤ ᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
ᠶᠡᠷᠦᠩᠬᠡᠢᠢ ᠳ᠋ᠦ ᠪᠡᠨ ᠺᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠷ ᠦᠷᠡᠵᠢᠯᠭᠦᠯᠬᠦ ᠢᠨᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭᠠᠨ ᠤ ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲ ᠢᠢᠠᠷ ᠡᠷᠭᠢᠭᠦᠯᠵᠦ᠂ ᠴᠠᠷ ᠬᠡᠮᠵᠢᠶ ᠡ᠋ ᠪᠡᠷ ᠢᠨᠦ ᠤᠷᠲᠤ ᠢᠢ ᠴᠢᠴᠠᠤᠯᠠᠬᠤ ᠦᠢᠯᠡᠳᠦᠯ ᠪᠣᠯᠤᠨᠠ᠃
ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭᠠᠨ ᠤ ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲ ᠭᠡᠳᠡᠭ ᠢᠨᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠤ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠠ ᠡᠬᠢᠯᠠᠯ ᠴᠡᠭ ᠢ ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭᠠᠨ z ᠲᠡᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠪᠠᠢᠢᠭᠠ ᠱᠤᠭᠤᠮ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠢᠢᠨ ᠥᠨᠴᠦᠭ φ ᠶᠤᠮ᠃
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ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠ ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠠ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰcomplex ᠲᠣᠭᠠ ᠢᠢᠨ ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲargument ᠨᠢ ᠥᠨᠴᠦᠭ φ᠃ |
ᠬᠡᠷᠡᠭᠯᠡᠭᠡ
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠢᠢ i ᠦᠰᠦᠭ ᠢᠢᠡᠷ ᠲᠡᠮᠳᠡᠭᠯᠡᠬᠦ ᠠᠭᠠᠳ ᠧᠯᠧᠺᠲ᠋ᠷᠣᠨᠢᠭ᠌ ᠲᠦelectronic j ᠦᠰᠦᠭ ᠢᠢᠡᠷ ᠲᠡᠮᠳᠡᠭᠯᠡᠨ ᠡ᠋᠃
ᠡᠨᠡ ᠢᠨᠦ i ᠦᠰᠦᠭ ᠢᠢᠡᠷ ᠲᠡᠮᠳᠡᠭᠯᠡᠳᠡᠭ ᠴᠠᠬᠢᠯᠭᠠᠨᠭᠦᠶᠦᠳᠦᠯ ᠡᠴᠡ ᠢᠯᠭᠠᠬᠤ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ ᠠ᠋ ᠡᠴᠡ ᠤᠷᠭᠠᠨ ᠭᠠᠷᠤᠭᠰᠠᠨ ᠤᠯᠠᠮᠵᠢᠯᠠᠯ ᠶᠤᠮ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠧᠯᠧᠺᠲ᠋ᠷᠣᠨᠢᠭ᠌ ᠲᠦ᠂ ᠢᠯᠠᠩᠭᠤᠶ ᠠ᠋ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠦᠯ ᠳ᠋ᠦ ᠣᠩᠴᠤᠭᠤᠢ ᠠᠴᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠯ ᠲᠠᠢ᠃
ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠦᠯ ᠰᠢᠨᠦ᠋ᠰsinus ᠳᠣᠯᠭᠢᠶᠠᠨ ᠳᠤ ᠨᠡᠮᠡᠬᠦ ᠪᠠ ᠬᠠᠰᠤᠬᠤ ᠢᠢᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠰᠣᠯᠢᠭᠳᠠᠳᠠᠭ᠃[2]
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ᠬᠦᠪᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠪᠦᠬᠦᠢ ᠡᠷᠴᠢᠮ ᠬᠦᠴᠦ᠃ P ᠢᠨᠦ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ Q ᠢᠨᠦ ᠬᠠᠷᠢᠭᠤ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ S ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠴᠢᠳᠠᠯ᠃ |
ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠶᠠᠪ ᠴᠠᠪ ᠲᠠᠭᠠᠷᠠᠭᠤᠯᠬᠤ ᠬᠡᠴᠡᠭᠦ ᠲᠤᠯᠠ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠦᠯ ᠦᠳ ᠢ ᠳᠠᠪᠬᠤᠷᠯᠠᠬᠤ ᠨᠡᠨ ᠲᠦᠪᠡᠭ ᠲᠡᠢ᠃
ᠬᠠᠷᠢᠨ ᠲᠥᠰᠦᠭᠡᠯᠡᠯ ᠭᠦᠶᠦᠳᠦᠯ ᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠨᠤᠭᠤᠳ ᠲᠠᠶ ᠬᠣᠣᠰᠮᠠᠭᠯᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠢᠢᠠᠷ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠦᠯ ᠦᠨ ᠲᠣᠭᠠᠴᠠᠭ ᠠ᠋ ᠬᠢᠵᠦ᠂ ᠴᠠᠬᠢᠯᠭᠠᠨ ᠤ ᠣᠰᠤᠯ ᠡᠴᠡ ᠤᠷᠢᠳᠤᠴᠢᠯᠠᠨᠰᠡᠷᠭᠡᠢᠢᠯᠬᠦ ᠲᠤᠰᠠ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠠᠭ ᠠ᠋ ᠢᠢ ᠮᠥᠨ ᠰᠢᠭ᠌ᠨᠠᠯsignal ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠭᠤᠯᠬᠤ ᠲᠧᠺᠨᠣᠯᠣᠭᠢ ᠳ᠋ᠤtechnology ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃
ᠡᠨᠡ ᠨᠢ ᠡᠭᠦᠷᠦᠨ ᠬᠣᠯᠪᠤᠭ ᠠ᠋᠂ ᠤᠲᠠᠰᠤ ᠦᠭᠡᠢ ᠳᠠᠮᠵᠢᠭᠤᠯᠤᠯᠲᠠ᠂ ᠷᠠᠳᠠᠷ᠂ ᠪᠢᠣᠯᠣᠭᠢ (ᠲᠠᠷᠢᠬᠢᠨ ᠤ ᠳᠣᠯᠭᠢᠶᠠᠨ) ᠰᠤᠳᠤᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠮᠢᠶᠠᠷᠠᠨ ᠠ᠋᠃
ᠶᠡᠷᠦ᠂ ᠰᠢᠨᠦ᠋ᠰ ᠪᠠ ᠺᠣᠰᠢᠨᠦ᠋ᠰ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠪᠦᠬᠦᠢ ᠵᠦᠢᠯ ᠢ ᠬᠡᠮᠵᠢᠬᠦ᠂ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠴᠢᠬᠤᠯᠠ ᠬᠡᠷᠡᠭ ᠲᠡᠢ᠃[1]
ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ
- ↑ 1.0 1.1 https://www.livescience.com/42748-imaginary-numbers.html Live Science. Elaine J. Hom. What Are Imaginary Numbers? 2014/01/22.
- ↑ https://www.electricaltechnology.org/2013/07/active-reactive-apparent-and-complex.html Electrical Technology. Active, Reactive, Apparent and Complex Power. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/07/31