引用:
原帖由 satsuki931000 於 2022-4-19 00:54 發表 ![](https://math.pro/db/images/common/back.gif)
6. 原式整理成\(\displaystyle |z_3-z_1|=(4+4i)|z_3-z_2|\)
令\(\displaystyle A(z_1) ,B(z_2),C(z_3)\)
畫圖得到\(\displaystyle \Delta{ABC}, \overline{BC}=x,\overline{AC}=4\sqrt{2}x,\overline{AB}=5\)
\(\d ...
感謝提供
這題我是用湊的,因為也還蠻好湊的
原式:\(z_1-(4+4i)z_2+(3+4i)z_3=0\)
\(\left((4+4i)-(3+4i)\right)z_1-(4+4i)z_2+(3+4i)z_3=0\)
\((4+4i)(z_1-z_2)+(3+4i)(z_3-z_1)=0\)
\(|4+4i|·|z_1-z_2|=|3+4i|·|z_3-z_1|\)
所以\(\displaystyle |z_3-z_1|=\frac{4\sqrt{2}}{5}·|z_1-z_2|=4\sqrt{2}\)