こんにちは。今回は複素数平面上で, 2直線のなす角を求めていきます。
複素数平面上の3点,
,
のつくる
の大きさを考えてみようと思います。
今, 点
![Rendered by QuickLaTeX.com \mathrm{B}(\beta)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-168c1d9f4d32b7d944f3bbdc22e0a800_l3.png)
![Rendered by QuickLaTeX.com \mathrm{A}(\alpha)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f358789f0ea0d1c97df70601ea69d18d_l3.png)
![Rendered by QuickLaTeX.com \theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-df36b52cea0081617d2fc178107fe54d_l3.png)
![Rendered by QuickLaTeX.com \mathrm{C}(\gamma)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-32ff97ce2435d5dd586047ca3483678b_l3.png)
![Rendered by QuickLaTeX.com \mathrm{B}(\beta)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-168c1d9f4d32b7d944f3bbdc22e0a800_l3.png)
![Rendered by QuickLaTeX.com \mathrm{A}(\alpha)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f358789f0ea0d1c97df70601ea69d18d_l3.png)
このとき, 点
![Rendered by QuickLaTeX.com \mathrm{C}'(\gamma-\alpha)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-c1c82be9209d4c4e3edef43d50a8251c_l3.png)
![Rendered by QuickLaTeX.com \mathrm{B}'(\beta-\alpha)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-b0db001e6b6f8ec8ae864fd9f240e625_l3.png)
![Rendered by QuickLaTeX.com \theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-df36b52cea0081617d2fc178107fe54d_l3.png)
![Rendered by QuickLaTeX.com \gamma-\alpha=(\cos\theta+i\sin\theta)(\beta-\alpha)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-0c1fd1266e820228acefc087cfbbc46d_l3.png)
この式の両辺を
![Rendered by QuickLaTeX.com \beta-\alpha](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-3db923d8a77a1234d1692966f7e6a31f_l3.png)
![Rendered by QuickLaTeX.com \dfrac{\gamma-\alpha}{\beta-\alpha}=\cos\theta+i\sin\theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-4e6d1c74b08d45ff0d5ec3a94b043507_l3.png)
となり,
![Rendered by QuickLaTeX.com \theta=\mathrm{arg}\, \dfrac{\gamma-\alpha}{\beta-\alpha}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-62fd73f077643d662264cb1563fff3ae_l3.png)
したがって,
![Rendered by QuickLaTeX.com \dfrac{\gamma-\alpha}{\beta-\alpha}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-01ccc8444ab4cb8cb21e27cc969969af_l3.png)
![Rendered by QuickLaTeX.com \theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-df36b52cea0081617d2fc178107fe54d_l3.png)
【問】複素数平面上の3点, ,
,
について,
の大きさを求めよ。
,
,
とするとき,
よって,
![](https://mathtext.info/blog/wordpress/wp-content/uploads/2022/04/f3tensuichokumekataukai-160x92.png)
こんにちは。今回は複素数平面上で, 2直線のなす角を求めていきます。
複素数平面上の3点,
,
のつくる
の大きさを考えてみようと思います。
【問】複素数平面上の3点, ,
,
について,
の大きさを求めよ。
,
,
とするとき,
よって,