ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ: Засвар хоорондын ялгаа
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ᠡᠭᠦᠨ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;">''k'' ∈ ℤ</span> ᠪᠤᠶᠤ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ᠃ | ᠡᠭᠦᠨ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;">''k'' ∈ ℤ</span> ᠪᠤᠶᠤ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ᠃ | ||
<span style="writing-mode: horizontal-tb;">''k'' = 0</span> ᠨᠥᠭᠦᠴᠡᠯ ᠳ᠋ᠦ ᠦᠨᠳᠢᠰᠦᠨ ᠤᠳᠬ ᠠ᠋ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>e</i><sup>−''π''/2</sup></span> ᠪᠤᠶᠤ ᠣᠢᠢᠷᠠᠯᠴᠠᠭ ᠠ᠋ ᠪᠠᠷ <span style="writing-mode: horizontal-tb;">0.207879576</span> ᠪᠣᠯᠤᠨ ᠠ᠋᠃<ref> | <span style="writing-mode: horizontal-tb;">''k'' = 0</span> ᠨᠥᠭᠦᠴᠡᠯ ᠳ᠋ᠦ ᠦᠨᠳᠢᠰᠦᠨ ᠤᠳᠬ ᠠ᠋ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>e</i><sup>−''π''/2</sup></span> ᠪᠤᠶᠤ ᠣᠢᠢᠷᠠᠯᠴᠠᠭ ᠠ᠋ ᠪᠠᠷ <span style="writing-mode: horizontal-tb;">0.207879576</span> ᠪᠣᠯᠤᠨ ᠠ᠋᠃<ref>David Wells. The Penguin Dictionary of Curious and Interesting Numbers. UK: Penguin Books 1997. ISBN=0-14-026149-4</ref><ref>Brilliant. What is i to the power of i. https://brilliant.org/discussions/thread/what-is-i-to-the-power-of-i-T. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/017/04</ref> | ||
===ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠡᠴᠡ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ=== | ===ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠡᠴᠡ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ=== | ||
ᠢᠵᠠᠭᠤᠷ | <span style="writing-mode: horizontal-tb;"><i>i</i></span> ᠲᠣᠭᠠᠨ ᠤ <span style="writing-mode: horizontal-tb;"><i>n</i></span> ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠨᠢ <span style="writing-mode: horizontal-tb;"><i>n</i></span> ᠲᠣᠭᠠᠨ ᠤ ᠬᠠᠷᠢᠭᠤ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠃ | ||
ᠬᠡᠳᠦᠨ ᠬᠠᠷᠢᠭᠤ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ᠋ ᠢᠢᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠳ᠋ᠤ ᠭᠠᠷᠬᠤ <span style="writing-mode: horizontal-tb;"><i>n</i></span>-ᠥᠨᠴᠦᠭᠲᠦ ᠢᠢᠨ ᠥᠨᠴᠦᠭ ᠦᠨ ᠲᠣᠭ ᠠ᠋ ᠪᠠᠷ ᠪᠠᠢᠢᠨ ᠠ᠋᠃<br><br> | |||
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<br><small><math>u_k=\cos {\frac{{\frac{\pi}{2}} + 2\pi k}{n}} +i\ \sin {\frac{{\frac{\pi}{2}} + 2\pi k}{n}},</math> </small> | |||
<br><br><small><math>\quad k=0,1,...,n-1</math> </small> | |||
<br><br><span style="writing-mode: vertical-lr;"><math>i</math> ᠲᠣᠭᠠᠨ ᠤ <br>ᠺᠸᠠᠲᠷᠠᠲ <br>ᠢᠵᠠᠭᠤᠷ᠄</span> | |||
<br><small><math>\{\sqrt i\} = \left\{\frac{1+i}\sqrt2; ~\frac{-1-i}\sqrt2 \right\}</math> </small> | |||
<br><br><span style="writing-mode: vertical-lr;"><math>i</math> ᠲᠣᠭᠠᠨ ᠤ <br>ᠺᠦᠪ <br>ᠢᠵᠠᠭᠤᠷ᠄</span> | |||
<br><small><math>\{\sqrt[3]i\} = \left\{-i;~\frac{i+\sqrt3}2;~ \frac{i-\sqrt3}2\right\}.</math></small> | |||
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