ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ: Засвар хоорондын ялгаа
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| 23-р мөр: | 23-р мөр: | ||
=== ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ === | === ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ === | ||
ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠷᠴᠡ ᠪᠤᠶᠤ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠳ᠋ᠦ ᠦᠷᠵᠢᠬᠦᠯᠦᠭᠰᠡᠨ ᠢᠢᠡᠷ᠄ | ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠ ᠢᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠷᠴᠡ ᠪᠤᠶᠤ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠳ᠋ᠦ ᠦᠷᠵᠢᠬᠦᠯᠦᠭᠰᠡᠨ ᠢᠢᠡᠷ᠄ | ||
<br><br> | |||
:<math>i\,(a + bi) = ai + bi^2 = -b + ai</math> | <span style="writing-mode: horizontal-tb;"> | ||
<br><math>i\,(a + bi)</math> | |||
<br><math> = ai + bi^2</math> | |||
<br><math> = -b + ai</math> | |||
</span> | |||
ᠭᠠᠷᠤᠮᠤᠢ᠃ | ᠭᠠᠷᠤᠮᠤᠢ᠃ | ||
| 31-р мөр: | 36-р мөр: | ||
ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠳ᠋ᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠤ ᠤᠷᠪᠠᠭᠤ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠲᠡᠢ ᠭᠠᠷ ᠨᠢᠭᠡᠨ: | ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠳ᠋ᠦ ᠬᠤᠪᠢᠶᠠᠬᠤ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠤ ᠤᠷᠪᠠᠭᠤ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠦᠷᠵᠢᠭᠦᠯᠬᠦ ᠲᠡᠢ ᠭᠠᠷ ᠨᠢᠭᠡᠨ: | ||
<br><br> | |||
<span style="writing-mode: horizontal-tb;"> | |||
<br><math>\frac{1}{i} = \frac{1}{i} \cdot \frac{i}{i}</math> | |||
<br><math> = \frac{i}{i^2} = \frac{i}{-1}</math> | |||
<br><math> = -i</math> | |||
</span> | |||
ᠡᠭᠦᠨ ᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠬᠡᠷᠡᠭᠯᠡᠪᠡᠰᠦ: | ᠡᠭᠦᠨ ᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ᠳ᠋ᠤ ᠬᠡᠷᠡᠭᠯᠡᠪᠡᠰᠦ: | ||
<br><br> | |||
<span style="writing-mode: horizontal-tb;"> | |||
<br><math>\frac{a + bi}{i} = -i\,(a + bi)</math> | |||
<br><math> = -a i - bi^2 = b - a i~.</math> | |||
</span> | |||
ᠡᠨᠡ ᠨᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠸᠧᠺᠲ᠋ᠣᠷ ᠢ<sup>vector</sup> ᠨᠠᠷᠠ ᠵᠥᠪ 90°ᠡᠷᠭᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠲᠡᠢ ᠠᠭᠠᠷ ᠨᠢᠭᠡᠨ ᠪᠤᠶ ᠠ᠋᠃ | ᠡᠨᠡ ᠨᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠡᠬᠢᠯᠡᠯ ᠴᠡᠭ ᠢ ᠲᠣᠭᠤᠷᠢᠭᠤᠯᠤᠨ ᠸᠧᠺᠲ᠋ᠣᠷ ᠢ<sup>vector</sup> ᠨᠠᠷᠠ ᠵᠥᠪ 90°ᠡᠷᠭᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠲᠡᠢ ᠠᠭᠠᠷ ᠨᠢᠭᠡᠨ ᠪᠤᠶ ᠠ᠋᠃ | ||
| 125-р мөр: | 139-р мөр: | ||
===<math>i</math> ᠲᠣᠭᠠᠨ ᠡᠴᠡ <math>i</math> ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ=== | ===<math>i</math> ᠲᠣᠭᠠᠨ ᠡᠴᠡ <math>i</math> ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ=== | ||
<br> | |||
<span style="writing-mode: horizontal-tb;"> | |||
<br><math>\sqrt[i]{i} | |||
= i^{\frac{1}{i}\frac{i}{i}} | = i^{\frac{1}{i}\frac{i}{i}} | ||
= i^{-i} | = i^{-i}</math> | ||
= \biggl(e^{{i}\frac{\pi}{2}}\biggr)^{-i} | <br><math>= \biggl(e^{{i}\frac{\pi}{2}}\biggr)^{-i}</math> | ||
= e^{-i^2\frac{\pi}{2}} | <br><math>= e^{-i^2\frac{\pi}{2}} | ||
= e^{\frac{\pi}{2}}</math> | = e^{\frac{\pi}{2}}</math> | ||
</span> | |||
==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ||