ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ: Засвар хоорондын ялгаа
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| 42-р мөр: | 42-р мөр: | ||
===ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ=== | ===ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ=== | ||
ᠲᠣᠭᠠ ᠢᠢ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠨᠢ ᠮᠥᠴᠢᠯᠭᠡ ᠪᠡᠷ ᠳᠠᠪᠲᠠᠭᠳᠠᠬᠤ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠲᠠᠢ:<ref>MathBits Notebook. Cyclic Nature of the Powers of "''i ".''https://mathbitsnotebook.com/Algebra2/ComplexNumbers/CPPowers.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/07/03</ref> | <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠ ᠢᠢ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠨᠢ ᠮᠥᠴᠢᠯᠭᠡ ᠪᠡᠷ ᠳᠠᠪᠲᠠᠭᠳᠠᠬᠤ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠲᠠᠢ:<ref>MathBits Notebook. Cyclic Nature of the Powers of "''i ".''https://mathbitsnotebook.com/Algebra2/ComplexNumbers/CPPowers.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/07/03</ref> | ||
| 60-р мөр: | 60-р мөр: | ||
|<span style="writing-mode: horizontal-tb;"> i<sup>8</sup> = i<sup>4</sup> • i<sup>4</sup> = 1 • 1 = 1 | |<span style="writing-mode: horizontal-tb;"> i<sup>8</sup> = i<sup>4</sup> • i<sup>4</sup> = 1 • 1 = 1 | ||
|<span style="writing-mode: horizontal-tb;"> i<sup>9</sup>= i<sup>4</sup> • i<sup>4</sup> • i = 1 • 1• i = i | |<span style="writing-mode: horizontal-tb;"> i<sup>9</sup>= i<sup>4</sup> • i<sup>4</sup> • i = 1 • 1• i = i | ||
|<span style="writing-mode: horizontal-tb;"> i<sup>10</sup> = (i<sup>4</sup>)<sup>2</sup> • i<sup>2</sup> = 1 • (-1) =-1 | |<span style="writing-mode: horizontal-tb;"> i<sup>10</sup> = (i<sup>4</sup>)<sup>2</sup> • i<sup>2</sup> = 1 • (-1) = -1 | ||
|<span style="writing-mode: horizontal-tb;"> i<sup>11</sup> = (i<sup>4</sup>)<sup>2</sup> • i<sup>3</sup> = 1 • (-i) = -i | |<span style="writing-mode: horizontal-tb;"> i<sup>11</sup> = (i<sup>4</sup>)<sup>2</sup> • i<sup>3</sup> = 1 • (-i) = -i | ||
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ᠡᠭᠦᠨ ᠢ ᠶᠡᠷᠦᠩᠬᠡᠢᠢᠯᠡᠭᠰᠡᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠪᠡᠷ ᠪᠢᠴᠢᠪᠡᠯ᠄ | |||
<span style="writing-mode: horizontal-tb;"> | |||
<br><math>i^{4n} = 1</math> | |||
<br><math>i^{4n+1} = i</math> | |||
<br><math>i^{4n+2} = -1</math> | |||
<br><math>i^{4n+3} = -i</math> | |||
</span> | |||
ᠡ᠊ᠨᠳᠡ ᠡᠴᠡ᠄ | |||
:<math>i^n = i^{(n \bmod 4)}</math> | |||
ᠡᠩ ᠦᠨ ᠢᠢᠡᠷ ᠠᠷᠭᠠᠴᠢᠯᠠᠪᠠᠰᠤ᠂ <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠤ ᠵᠡᠷᠭᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠶᠢᠯᠠᠬᠤ ᠢᠢᠨ ᠲᠤᠯᠠᠳᠠ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠦᠵᠡᠭᠦᠯᠦᠭᠴᠢ ᠢᠢ<ref>ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ᠃ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠮᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ᠃ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠪᠣᠲᠢ᠃ ᠪᠦ᠊᠂ ᠨᠠ᠊᠂ ᠮᠣ᠊᠂ ᠠ᠊᠂ ᠤ᠊᠂ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠬᠡᠯᠡ ᠵᠣᠬᠢᠶᠠᠯ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ ᠤᠯᠤᠰ ᠤᠨ ᠬᠡᠪᠯᠡᠯ ᠦᠨ ᠭᠠᠵᠠᠷ᠃ ᠤᠯᠠᠭᠠᠨᠪᠠᠭᠠᠲᠤᠷ 1970᠃</ref> <span style="writing-mode: horizontal-tb;">4</span> ᠳ᠋ᠦ ᠬᠤᠪᠢᠶᠠᠮᠤᠢ᠃ | |||
ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠢᠨᠦ <span style="writing-mode: horizontal-tb;">0</span> ᠲᠡᠢ ᠲᠡᠩᠴᠡᠬᠦ ᠠᠪᠠᠰᠤ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠬᠠᠷᠢᠭᠤ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;">1</span>᠂ | |||
ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠢᠨᠦ <span style="writing-mode: horizontal-tb;">1</span> ᠲᠡᠢ ᠲᠡᠩᠴᠡᠬᠦ ᠠᠪᠠᠰᠤ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠬᠠᠷᠢᠭᠤ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;"><i>i</i></span>᠂ | |||
ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠢᠨᠦ <span style="writing-mode: horizontal-tb;">2</span> ᠲᠡᠢ ᠲᠡᠩᠴᠡᠬᠦ ᠠᠪᠠᠰᠤ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠬᠠᠷᠢᠭᠤ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;">-1</span>᠂ | |||
ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠢᠨᠦ <span style="writing-mode: horizontal-tb;">3</span> ᠲᠡᠢ ᠲᠡᠩᠴᠡᠬᠦ ᠠᠪᠠᠰᠤ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠦᠭᠰᠡᠨ ᠦ ᠬᠠᠷᠢᠭᠤ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;"><i>-i</i></span> | |||
ᠪᠠᠢᠢᠨᠠ ᠬᠡᠮᠡᠨ ᠲᠣᠭᠲᠠᠭᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃ | |||
==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | |||
ᠦᠵᠡᠭᠦᠯᠦᠭᠴᠢ - exponent - экспонента | |||
ᠦᠯᠡᠳᠡᠭᠳᠡᠯ - remainder - остаток | |||