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Mathematics
Mathematics
Problem
If
z
z
z
satisfies the inequality
∣
z
−
1
∣
<
∣
z
+
1
∣
|z - 1| < |z + 1|
∣
z
−
1∣
<
∣
z
+
1∣
, then one has a.
∣
z
−
2
−
i
∣
<
∣
z
+
2
−
i
∣
,
i
=
−
1
|z - 2 - i| < |z + 2 - i|, i = \sqrt{-1}
∣
z
−
2
−
i
∣
<
∣
z
+
2
−
i
∣
,
i
=
−
1
b.
∣
arg
(
z
+
i
)
∣
<
π
2
,
i
=
−
1
|\arg(z + i)| < \frac{\pi}{2}, i = \sqrt{-1}
∣
ar
g
(
z
+
i
)
∣
<
2
π
,
i
=
−
1
c.
Re
(
z
)
<
0
\operatorname{Re}(z) < 0
Re
(
z
)
<
0
d.
Im
(
i
z
ˉ
)
>
0
,
i
=
−
1
\operatorname{Im}(i\bar{z}) > 0, i = \sqrt{-1}
Im
(
i
z
ˉ
)
>
0
,
i
=
−
1
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