"ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠊ᠠ᠋"-ны өөр хувилбарууд
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ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠢᠨᠦ ᠲᠡᠭ <span style="writing-mode: horizontal-tb;"><i>(0)</i></span> ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ [[ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ]] ᠢᠢ '''ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋''' ᠬᠠᠮᠠᠮᠦᠢ᠃ | ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠢᠨᠦ ᠲᠡᠭ <span style="writing-mode: horizontal-tb;"><i>(0)</i></span> 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᠃<ref name=":0">https://www.livescience.com/42748-imaginary-numbers.html Live Science. Elaine J. Hom. What Are Imaginary Numbers? 2014/01/22. </ref> | ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠢᠢ ᠺᠸᠠᠲᠷᠠᠲ<sup>quadrate</sup> ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠬᠠᠰᠤᠬᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠢ ᠬᠠᠷᠢᠭᠤ ᠭᠠᠷᠤᠨ ᠠ᠋᠃<ref name=":0">https://www.livescience.com/42748-imaginary-numbers.html Live Science. Elaine J. Hom. What Are Imaginary Numbers? 2014/01/22. </ref> | ||
ᠲᠡᠭᠡᠬᠦ ᠪᠡᠷ ᠬᠠᠭᠤᠷᠮᠠᠭ | ᠲᠡᠭᠡᠬᠦ ᠪᠡᠷ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠠᠨᠤ ᠬᠠᠰᠤᠬᠤ ᠤᠳᠬ ᠠ᠋ ᠲᠠᠶ ᠲᠣᠭᠠᠨ ᠤ ᠬᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ ᠮᠥᠨ᠃ | ||
ᠬᠠᠭᠤᠷᠮᠠᠭ | ᠲᠡᠭ <span style="writing-mode: horizontal-tb;"><i>(0)</i></span> ᠲᠣᠭ ᠠ᠋ ᠪᠣᠳᠠᠲᠤ ᠪᠤᠶᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠠᠯᠢ ᠨᠢ ᠴᠤ ᠪᠠᠢᠢᠵᠤ ᠪᠣᠯᠤᠨ ᠠ᠋᠃ | ||
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== ᠳᠦᠷᠰᠦᠯᠡᠯ == | |||
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|style = "height: 150px;"|ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ ᠪᠦᠬᠦᠢ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠯ ᠤᠨ ᠳᠦᠷᠰᠦᠯᠡᠯ᠃ | |||
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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᠃ | |||
ᠶᠡᠷᠦ᠂ ᠰᠢᠨᠦ᠋ᠰ ᠪᠠ ᠺᠣᠰᠢᠨᠦ᠋ᠰ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠪᠦᠬᠦᠢ ᠵᠦᠢᠯ ᠢ ᠬᠡᠮᠵᠢᠬᠦ᠂ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ | ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;"><i>–1</i></span> ᠢᠢᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠰᠠᠨ <span style="writing-mode: horizontal-tb;"><i>180</i></span> ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠤᠨ ᠠ᠋᠃ | ||
<span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭ ᠠ᠋ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠯᠭᠦᠯᠬᠦ ᠢᠨᠦ ᠨᠠᠷᠠ ᠪᠤᠷᠤᠭᠤ “ᠡᠶᠡᠷᠭᠦ” ᠴᠢᠭ᠌ ᠲᠦ <span style="writing-mode: horizontal-tb;"><i>90</i></span> ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠬᠤ ᠪᠠ ᠬᠡᠷᠪᠡ <span style="writing-mode: horizontal-tb;"><i>i2 = -1</i></span> ᠭᠡᠰᠡᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠢᠨᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠰᠠᠨ <span style="writing-mode: horizontal-tb;"><i>90</i></span> ᠬᠡᠮ ᠦᠨ ᠬᠣᠶᠠᠷ ᠡᠷᠭᠢᠯᠲᠡ ᠭᠡᠵᠦ ᠦᠵᠡᠪᠡᠯ ᠦᠷ ᠡ᠋ ᠳ᠋ᠦ᠋ᠩ ᠢᠨᠦ ᠭᠠᠭᠴᠠ <span style="writing-mode: horizontal-tb;"><i>180</i></span> ᠬᠡᠮ ᠦᠨ ᠡᠷᠭᠢᠯᠲᠡ ᠪᠣᠯᠤᠨ ᠠ᠋᠃ | |||
“ᠰᠥᠷᠭᠦ” (ᠨᠠᠷᠠ ᠵᠥᠪ) ᠴᠢᠭ᠌ ᠲᠦ <span style="writing-mode: horizontal-tb;"><i>90</i></span> ᠬᠡᠮ ᠡᠷᠭᠢᠬᠦ ᠢᠨᠦ ᠮᠥᠨ ᠡᠨᠡ ᠳᠦᠷᠰᠦᠯᠡᠯ ᠳ᠋ᠦ ᠨᠡᠶ᠋ᠢᠴᠡᠬᠦ ᠪᠠ <span style="writing-mode: horizontal-tb;"><i>x2 = -1</i></span> ᠭᠡᠰᠡᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠰᠶ᠋ᠢᠳ <span style="writing-mode: horizontal-tb;"><i>−i</i></span> ᠪᠣᠯᠬᠤ ᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | |||
ᠶᠡᠷᠦᠩᠬᠡᠢᠢ ᠳ᠋ᠦ ᠪᠡᠨ ᠺᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠷ ᠦᠷᠡᠵᠢᠯᠭᠦᠯᠬᠦ ᠢᠨᠦ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰ ᠲᠣᠭᠠᠨ ᠤ ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲ<sup>argument</sup> 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 <span style="writing-mode: horizontal-tb;"><i>φ</i></span> ᠶᠤᠮ᠃ | |||
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|style = "height: 150px;"|ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠ ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠠ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭᠠ ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠻᠣᠮᠫ᠊ᠯᠧᠻᠰ<sup>complex</sup> ᠲᠣᠭᠠ ᠢᠢᠨ ᠠᠷᠭᠤᠮᠧᠨ᠍ᠲ<sup>argument</sup> ᠨᠢ ᠥᠨᠴᠦᠭ <span style="writing-mode: horizontal-tb;"><i>φ</i></span>᠃ | |||
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==ᠬᠡᠷᠡᠭᠯᠡᠭᠡ== | |||
[[ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ]] ᠢᠢ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠦᠰᠦᠭ ᠢᠢᠡᠷ ᠲᠡᠮᠳᠡᠭᠯᠡᠬᠦ ᠠᠭᠠᠳ ᠧᠯᠧᠺᠲ᠋ᠷᠣᠨᠢᠭ᠌ ᠲᠦ<sup>electronic</sup> <span style="writing-mode: horizontal-tb;"><i>j</i></span> ᠦᠰᠦᠭ ᠢᠢᠡᠷ ᠲᠡᠮᠳᠡᠭᠯᠡᠨ ᠡ᠋᠃ | |||
ᠡᠨᠡ ᠢᠨᠦ <span style="writing-mode: horizontal-tb;"><i>i</i></span> 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 ᠰᠢᠨᠦ᠋ᠰ<sup>sinus</sup> ᠳᠣᠯᠭᠢᠶᠠᠨ ᠳᠤ ᠨᠡᠮᠡᠬᠦ ᠪᠠ ᠬᠠᠰᠤᠬᠤ ᠢᠢᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠰᠣᠯᠢᠭᠳᠠᠳᠠᠭ᠃<ref>https://www.electricaltechnology.org/2013/07/active-reactive-apparent-and-complex.html Electrical Technology. Active, Reactive, Apparent and Complex Power. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/07/31</ref> | |||
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|style = "height: 150px;"|ᠬᠤᠪᠢᠰᠬᠤ ᠭᠦᠶᠦᠳᠡᠯ ᠪᠦᠬᠦᠢ ᠡᠷᠴᠢᠮ ᠬᠦᠴᠦ᠃ <span style="writing-mode: horizontal-tb;"><i>P</i></span> ᠢᠨᠦ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ <span style="writing-mode: horizontal-tb;"><i>Q</i></span> ᠢᠨᠦ ᠬᠠᠷᠢᠭᠤ ᠢᠳᠡᠪᠬᠢᠲᠦ ᠴᠢᠳᠠᠯ᠂ <span style="writing-mode: horizontal-tb;"><i>S</i></span> ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ᠴᠢᠳᠠᠯ᠃ | |||
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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 ᠰᠢᠭ᠌ᠨᠠᠯ<sup>signal</sup> ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠭᠤᠯᠬᠤ ᠲᠧᠺᠨᠣᠯᠣᠭᠢ ᠳ᠋ᠤ<sup>technology</sup> ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃ | |||
ᠡᠨᠡ ᠨᠢ ᠡᠭᠦᠷ ᠦᠨ ᠬᠣᠯᠪᠤᠭ ᠠ᠋᠂ ᠤᠲᠠᠰᠤ ᠦᠭᠡᠢ ᠳᠠᠮᠵᠢᠭᠤᠯᠤᠯᠲᠠ᠂ ᠷᠠᠳᠠᠷ<sup>radar</sup>᠂ ᠪᠢᠣᠯᠣᠭᠢ<sup>biology</sup> (ᠲᠠᠷᠢᠬᠢᠨ ᠤ ᠳᠣᠯᠭᠢᠶᠠᠨ) ᠰᠤᠳᠤᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠮᠢᠶᠠᠷᠤᠨ ᠠ᠋᠃ | |||
ᠶᠡᠷᠦ᠂ ᠰᠢᠨᠦ᠋ᠰ ᠪᠠ ᠺᠣᠰᠢᠨᠦ᠋ᠰ<sup>cosinus</sup> ᠳᠣᠯᠭᠢᠶᠠᠨ ᠪᠦᠬᠦᠢ ᠵᠦᠢᠯ ᠢ ᠬᠡᠮᠵᠢᠬᠦ᠂ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠬᠤ ᠳ᠋ᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ ᠠ᠋ ᠴᠢᠬᠤᠯᠠ ᠬᠡᠷᠡᠭ ᠲᠡᠢ᠃<ref name=":0" /> | |||
==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== | |||
<div style="writing-mode: horizontal-tb; "><References/> | |||
[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]] | |||
12:59, 11 Аравдугаар сар 2021-ий байдлаарх одоогийн засвар
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[засварлах | кодоор засварлах]
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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[засварлах | кодоор засварлах]
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[засварлах | кодоор засварлах]
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[засварлах | кодоор засварлах]
- ↑ 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