ans

02010
$6$或$-2+12\mathrm{i}$或$2-8\mathrm{i}$

002020
$1+\dfrac{14}5\mathrm{i}$

003521
$\dfrac\pi 2$

002018
$4$

003524
(1) 直线$y=0$; (2) 圆$(x+1)^2+y^2=1$; (3) 椭圆$\dfrac{x^2}{36}+\dfrac{y^2}{11}=1$; (4) 线段$y=0 \ (x\in [-1,1])$; (5) 双曲线的一支: $y^2-\dfrac{x^2}{3}=1 \ (y<0)$

003534
(1) $[4\sqrt{2}-2,4\sqrt{2}+2]$; (2) $(3+\sqrt{2})-(4+\sqrt{2})\mathrm{i}$

003535
以$(1,0)$为圆心, $\dfrac 12$为半径的圆

002057
$2+\mathrm{i}$与$-2-\mathrm{i}$

003542
\textcircled{2}\textcircled{5}

000168
(1) 解为$2+\mathrm{i}$与$2-\mathrm{i}$; (2) 解为$\dfrac{-1+\sqrt{10}}3$与$\dfrac{-1-\sqrt{10}}3$

030110
(1) $-1\pm \dfrac{\sqrt{2}}2\mathrm{i}$; (2) $2(x+1+\dfrac{\sqrt{2}}2\mathrm{i})(x+1-\dfrac{\sqrt{2}}2\mathrm{i})$

003544
$p=12$, $q=26$

002085
证明略

002086
$\dfrac 52$或$-2$

000163
(1) $11$, $-60$, $61$, $11+60\mathrm{i}$; (2) \textcircled{3}

003519
B

003520
A

003523
$a+b\mathrm{i}$

003522
$-2+\mathrm{i}$

002012
二

002016
$\{-2,0\}$

002017
$40$

003528
以$(-3,7)$为圆心, $12$为半径的圆

007313
$3+2\mathrm{i}$与$-3-2\mathrm{i}$

007314
解为$\dfrac{\sqrt{2}}2+\dfrac{\sqrt{2}}2\mathrm{i}$与$-\dfrac{\sqrt{2}}2-\dfrac{\sqrt{2}}2\mathrm{i}$

003758
不存在推出关系, 因为$P$成立当且仅当$a\in (-2\sqrt{2},2\sqrt{2})$, $Q$成立当且仅当$a\in [-3,-1]\cup [1,3]$, $a=0$时$P$成立但$Q$不成立, $a=3$时$Q$成立但$P$不成立

004167
$2\sqrt{3}$

009032
(1) $(x+\sqrt{5}\mathrm{i}y)(x-\sqrt{5}\mathrm{i}y)$; (2) $2(x-\dfrac{3+\mathrm{i}}2)(x-\dfrac{3-\mathrm{i}}2)$

003551
(1) $-\dfrac 14$或$\dfrac{17}{4}$; (2) $-\dfrac 14$或$\dfrac 94$