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Joint Entrance Examination
Mathematics
Complex Numbers
Question 14
Question 14 of 455
Medium
MCQ
Let
S
=
z
:
3
⩽
∣
2
z
−
3
(
1
+
i
)
∣
⩽
7
S={z:3\leqslant |2z-3(1+i)|\leqslant 7}
S
=
z
:
3
⩽
∣2
z
−
3
(
1
+
i
)
∣
⩽
7
be a set of complex numbers. Then
M
i
n
z
∈
S
∣
(
z
+
1
2
(
5
+
3
i
)
)
∣
{Min}_{z\in S}|(z+\frac{1}{2}(5+3i))|
M
in
z
∈
S
∣
(
z
+
2
1
(
5
+
3
i
))
∣
is equal to :
A
1
2
\frac{1}{2}
2
1
B
5
2
\frac{5}{2}
2
5
C
2
D
3
2
\frac{3}{2}
2
3
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Official solution
3
2
≤
∣
z
−
(
3
2
+
3
2
i
)
∣
≤
7
2
\frac{3}{2}\le |z-(\frac{3}{2}+\frac{3}{2}i)|\le \frac{7}{2}
2
3
≤
∣
z
−
(
2
3
+
2
3
i
)
∣
≤
2
7
=
16
+
9
−
7
2
=
5
−
7
2
=
3
2
\begin{gathered} =\sqrt{16+9}-\frac{7}{2} \\ =5-\frac{7}{2} \\ =\frac{3}{2} \end{gathered}
=
16
+
9
−
2
7
=
5
−
2
7
=
2
3
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