From 12f72aae9b927ddc8dca38f6bab58a6d6c1d507b Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Sat, 18 May 2024 21:10:44 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A526=E5=B1=8A=E4=B8=80=E4=BA=9B?=
 =?UTF-8?q?=E7=AD=94=E6=A1=88?=
MIME-Version: 1.0
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---
 工具v4/文本文件/metadata.txt | 186 +++++++++++++++++------------------
 1 file changed, 93 insertions(+), 93 deletions(-)

diff --git a/工具v4/文本文件/metadata.txt b/工具v4/文本文件/metadata.txt
index 00794e2f..997d6264 100644
--- a/工具v4/文本文件/metadata.txt
+++ b/工具v4/文本文件/metadata.txt
@@ -1,116 +1,116 @@
 ans
 
-018529
-(1) $-3+5\mathrm{i}$; (2) $-4\mathrm{i}$; (3) $14-8\mathrm{i}$; (4) $-25\mathrm{i}$
+024831
+$\dfrac{2}{5}$
 
-018530
-(1) $1+\mathrm{i}$; (2) $-\dfrac{1}{3}+\dfrac{2\sqrt{2}}{3}\mathrm{i}$
+024832
+$2(\cos\dfrac{2\pi}{3}+\mathrm{i}\sin\dfrac{2\pi}{3})$
 
-018531
-$\mathrm{i}^{4k+1}=\mathrm{i}$, $\mathrm{i}^{4k+2}=-1$, $\mathrm{i}^{4k+3}=-\mathrm{i}$, $\mathrm{i}^{4k}=1$, $k\in \mathbf{Z}$
+024833
+$\pm \sqrt{2}\mathrm{i}$
 
-018532
+024834
+$\pm \dfrac{1}{2}$
+
+024830
+$2(x+1-\dfrac{\sqrt{2}}{2}\mathrm{i})(x+1+\dfrac{\sqrt{2}}{2}\mathrm{i})$
+
+024835
+$\dfrac{\pi}{4}$
+
+024836
+$2$
+
+024837
+\textcircled{3}\textcircled{5}
+
+024838
+$9+\sqrt{2}$
+
+024839
+$-\dfrac{15}{2}\pm \dfrac{15\sqrt{3}}{2}\mathrm{i}$
+
+040857
+(1) $m=-1$, $|z|=\sqrt{2}$; (2) $(-1,1)$
+
+040858
+(1) $m=-2$; (2) $m=\pm 2\sqrt{6}$或$\pm 4\sqrt{3}$
+
+040799
+$-1-\mathrm{i}$
+
+040800
+$1+\mathrm{i}$
+
+040802
+$-1$
+
+040792
+$4\pi$
+
+040803
+$\pm\sqrt{3}$
+
+040804
+\textcircled{4}
+
+040805
+内心
+
+040807
+C
+
+040808
+$|z|$的最小值为$\dfrac{12}{5}$, 此时$z=\dfrac{48}{25}+\dfrac{36}{25}\mathrm{i}$
+
+024822
 $0$
 
-018533
-$4ab\mathrm{i}$
+040753
+$-\mathrm{i}$
 
-018534
-$-2$
+024823
+$1$
 
-018535
-$3$
+040754
+$1+2\mathrm{i}$
 
-018536
-\begin{tabular}{|c|c|c|c|c|c|c|}
-\hline$z$ & 是否复数 & 是否实数 & 是否虚数 & 是否纯虚数 & $\mathrm{Re} z$ & $\mathrm{Im} z$ \\
-\hline$-0.5 \mathrm{i}$ & 是 & 否 & 是 & 是 & $0$ & $-0.5$ \\
-\hline $\frac{1}{2}-\sqrt{2} \mathrm{i}$ & 是 & 否 & 是 & 否 & $\dfrac{1}{2}$ & $-\sqrt{2}$\\
-\hline $\pi$ & 是 & 是 & 否 & 否 & $\pi$ & $0$ \\
-\hline $0$ & 是 & 是 & 否 & 否 & $0$ & $0$ \\
-\hline $\sqrt{3}$ & 是 & 是 & 否 & 否 & $\sqrt{3}$ & $0$ \\
-\hline $2 \mathrm{i}-5$ & 是 & 否 & 是 & 否 & $-5$ & $2$ \\
-\hline
-\end{tabular}
+024824
+$\dfrac{\sqrt{10}}{10}$
 
-018537
-(1) $m=1$或$-1$; (2) $m<-1$或$-1<m<1$或$m>1$; (3) $m=-2$; (4) $m=1$
+040758
+$(-\sqrt{3},\sqrt{3})$
 
-018538
-证明略
+040760
+$7-\mathrm{i}$或$-7+\mathrm{i}$
 
-018539
-$-1-2\mathrm{i}$
+040801
+$2-\mathrm{i}$
 
-009647
-(1) 证明题, 理由略; (2) 假命题, $z=0$; (3) 真命题, 理由略; (4) 假命题, $z=0$
+040765
+外心
 
-009648
-(1) $m=1$; (2) $m\ne 1$; (3) $m=-2$
+040766
+\textcircled{2}\textcircled{4}
 
-018540
-(1) $\theta=\pm \dfrac{\pi}{6}+k\pi$, $k\in \mathbf{Z}$; (2) $\theta=k\pi$, $k\in \mathbf{Z}$; (3) $\theta=\dfrac{\pi}{6}+2k\pi$或$\dfrac{5\pi}{6}+2k\pi$, $k\in \mathbf{Z}$
+040806
+C
 
-018543
-$z_B-z_A$
+040768
+B
 
-018544
-证明略
+024826
+$\sqrt{14}$
 
-018545
-$2+3\mathrm{i}$
+024827
+$[-\dfrac{2}{5},0]$
 
-009649
-(1) $x$轴的正半轴; (2) $x$轴的负半轴; (3) 第二象限; (4) $y$轴的负半轴
+024828
+$6$
 
-009651
-$\overrightarrow{AB}$对应的复数为$2-2\mathrm{i}$, $\overrightarrow{BA}$对应的复数为$-2+2\mathrm{i}$
+040770
+(1) $z\cdot \overline{z}=1$, $\text{Re} z$的范围为$(-\dfrac{1}{2},1)$; (2) 证明略
 
-009652
-$(-1,3)$
-
-018546
-$3+\mathrm{i}$
-
-018547
-$4-2\mathrm{i}$
-
-018548
-证明略
-
-018549
-(1) $\dfrac{\sqrt{10}}{5}$; (2) $1$
-
-018550
-$3\sqrt{2}$
-
-018551
-$[\dfrac{12}{5},4]$
-
-018552
-(1) $\dfrac{\pi}{2}$; (2) $\dfrac{1}{2}$
-
-009654
-$Z_1$在圆上, $Z_2$在圆内
-
-009655
-$\sqrt{2}$
-
-009656
-$\sqrt{65}$
-
-018567
-$1$和$-\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}\mathrm{i}$
-
-024820
-$\sqrt{13}$
-
-017652
-(1) $(4,2)$; (2) $-\dfrac{4\sqrt{17}}{17}$
-
-024818
-(1) $-\dfrac{\sqrt{2}}{2}$; (2) $\sqrt{29}$; (3) $-\dfrac{23}{3}$; (4) $(-\dfrac{23}{3},2)\cup (2,+\infty)$
-
-024819
-(1) $\cos\theta$; (2i) $(0,3)$; (2ii) $2\sqrt{3}-3$
+040771
+(1) $-1-\mathrm{i}$; (2) $(-1,-\dfrac{1}{2}]\cup [-\dfrac{1}{5},+\infty)$