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Joint Entrance Examination
Mathematics
Complex Numbers
Question 375
Question 375 of 455
Medium
MCQ
If
∣
z
−
4
∣
<
∣
z
−
2
∣
|z-4|<|z-2|
∣
z
−
4∣
<
∣
z
−
2∣
, its solution is given by
A
Re
(
z
)
>
0
\operatorname{Re}(z)>0
Re
(
z
)
>
0
B
Re
(
z
)
<
0
\operatorname{Re}(z)<0
Re
(
z
)
<
0
C
Re
(
z
)
>
3
\operatorname{Re}(z)>3
Re
(
z
)
>
3
D
Re
(
z
)
>
2
\operatorname{Re}(z)>2
Re
(
z
)
>
2
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Solutions · 1
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Official solution
With
z
=
x
+
i
y
z=x+iy
z
=
x
+
i
y
:
(
x
−
4
)
2
<
(
x
−
2
)
2
⟹
−
8
x
+
16
<
−
4
x
+
4
⟹
12
<
4
x
⟹
x
>
3.
(x-4)^2<(x-2)^2 \implies -8x+16<-4x+4 \implies 12<4x \implies x>3.
(
x
−
4
)
2
<
(
x
−
2
)
2
⟹
−
8
x
+
16
<
−
4
x
+
4
⟹
12
<
4
x
⟹
x
>
3.
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