ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠊ᠠ᠋
ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠢᠨᠦ ᠲᠡᠭ (0) ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠬᠠᠮᠠᠮᠦᠢ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠺᠸᠠᠲᠷᠠᠲquadrate ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠬᠠᠰᠤᠬᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠬᠠᠷᠢᠭᠤ ᠭᠠᠷᠤᠨ ᠠ᠋᠃[1]
ᠲᠡᠭᠡᠬᠦ ᠪᠡᠷ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ 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 ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠠ ᠪᠣᠰᠤᠭ ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠡᠴᠡ ᠪᠦᠷᠢᠳᠦᠳᠡᠭ᠃
ᠬᠠᠭᠤᠷᠮᠠᠬ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠰᠤᠭ ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠪᠠᠢᠢᠷᠢᠰᠢᠳᠠᠭ᠃
ᠬᠡᠪᠲᠡᠭᠡ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠢᠢ 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 “ᠡᠶᠡᠷᠭᠦ” 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 ᠨᠡᠶ᠋ᠢᠴᠡᠬᠦ 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 ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲargument 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 ᠲᠣᠭᠠ 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 ᠴᠠᠬᠢᠯᠭᠠᠨ ᠭᠦᠶᠦᠳᠡᠯ ᠡᠴᠡ ᠢᠯᠭᠠᠬᠤ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ ᠠ᠋ ᠡᠴᠡ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠤᠭᠰᠠᠨ ᠤᠯᠠᠮᠵᠢᠯᠠᠯ ᠶᠤᠮ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠧᠯᠧᠺᠲ᠋ᠷᠣᠨᠢᠭ᠌ ᠲᠦ᠂ ᠢᠯᠠᠩᠭᠤᠶ ᠠ᠋ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠳ᠋ᠦ ᠣᠨᠴᠤᠭᠤᠢ ᠠᠴᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠯ ᠲᠠᠢ᠃
ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠰᠢᠨᠦ᠋ᠰsinus ᠳᠣᠯᠭᠢᠶᠠᠨ ᠳᠤ ᠨᠡᠮᠡᠬᠦ ᠪᠠ ᠬᠠᠰᠤᠬᠤ ᠢᠢᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠰᠣᠯᠢᠭᠳᠠᠳᠠᠭ᠃[2]
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ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠪᠦᠬᠦᠢ ᠡᠷᠴᠢᠮ ᠬᠦᠴᠦ᠃ P ᠢᠨᠦ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ Q ᠢᠨᠦ ᠬᠠᠷᠢᠭᠤ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ S ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ᠴᠢᠳᠠᠯ᠃ |
ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠶᠠᠪ ᠴᠠᠪ ᠲᠠᠭᠠᠷᠠᠭᠤᠯᠬᠤ ᠬᠡᠴᠡᠭᠦᠦ ᠲᠤᠯᠠ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠦᠳ ᠢ ᠳᠠᠪᠬᠤᠷᠯᠠᠬᠤ ᠨᠡᠨ ᠲᠦᠪᠡᠭ ᠲᠡᠢ᠃
ᠬᠠᠷᠢᠨ ᠲᠥᠰᠦᠭᠡᠯᠡᠯ ᠭᠦᠶᠦᠳᠡᠯ ᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ ᠠ᠋ ᠨᠤᠭᠤᠳ ᠲᠠᠶ ᠬᠣᠣᠰᠮᠠᠭᠯᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠢᠢᠠᠷ ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠦᠨ ᠲᠣᠭᠠᠴᠠᠭ ᠠ᠋ ᠬᠢᠵᠦ᠂ ᠴᠠᠬᠢᠯᠭᠠᠨ ᠤ ᠣᠰᠤᠯ ᠡᠴᠡ ᠤᠷᠢᠳᠤᠴᠢᠯᠠᠨ ᠰᠡᠷᠭᠡᠢᠢᠯᠡᠬᠦ ᠲᠤᠰᠠ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠮᠥᠨ ᠰᠢᠭ᠌ᠨᠠᠯsignal ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠭᠤᠯᠬᠤ ᠲᠧᠺᠨᠣᠯᠣᠭᠢ ᠳ᠋ᠤtechnology ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃
ᠡᠨᠡ ᠨᠢ ᠡᠭᠦᠷ ᠦᠨ ᠬᠣᠯᠪᠤᠭ ᠠ᠋᠂ ᠤᠲᠠᠰᠤ ᠦᠭᠡᠢ ᠳᠠᠮᠵᠢᠭᠤᠯᠤᠯᠲᠠ᠂ ᠷᠠᠳᠠᠷradar᠂ ᠪᠢᠣᠯᠣᠭᠢbiology (ᠲᠠᠷᠢᠬᠢᠨ ᠤ ᠳᠣᠯᠭᠢᠶᠠᠨ) ᠰᠤᠳᠤᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠮᠢᠶᠠᠷᠤᠨ ᠠ᠋᠃
ᠶᠡᠷᠦ᠂ ᠰᠢᠨᠦ᠋ᠰ ᠪᠠ ᠺᠣᠰᠢᠨᠦ᠋ᠰcosinus ᠳᠣᠯᠭᠢᠶᠠᠨ ᠪᠦᠬᠦᠢ ᠵᠦᠢᠯ ᠢ ᠬᠡᠮᠵᠢᠬᠦ᠂ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠴᠢᠬᠤᠯᠠ ᠬᠡᠷᠡᠭ ᠲᠡᠢ᠃[1]
ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ
ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠ - real number - действительное число
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ - imaginary unit - мнимая единица
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ - imaginary number - чисто мнимое число
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ - complex number - комплексное число
ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ - real part - действительная часть
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ - imaginaty part - мнимая часть
ᠲᠡᠩᠬᠡᠯᠢᠭ - axis - ось
ᠣᠯᠠᠨᠯᠢᠭ - set - множество
ᠡᠶᠡᠷᠭᠦ - positive - положительный
ᠰᠥᠷᠭᠦ - negative - отрицательный
ᠲᠡᠭᠰᠢᠳᠬᠡᠯ - equation - уравнение
ᠡᠷᠭᠢᠯᠲᠡ - rotation - поворот
ᠬᠡᠮ - degree - градус
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