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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 4 Questions
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© examsnet.com
Question : 8
Total: 37
The sum of the square of the modulus of the elements in the set
{
z
=
a
+
i
b
:
a
,
b
∈
Z
,
z
∈
C
,
|
z
−
1
|
≤
1
,
|
z
−
5
|
≤
z
−
5
i
|
}
is ______.
[9 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
|
z
−
1
|
≤
1
⇒
|
(
x
−
1
)
+
i
y
|
≤
1
⇒
√
(
x
−
1
)
2
+
y
2
≤
1
⇒
(
x
−
1
)
2
+
y
2
≤
1
.
.
.
. . . (1)
Also
|
z
−
5
|
≤
|
z
−
5
i
|
(
x
−
5
)
2
+
y
2
≤
x
2
+
(
y
−
5
)
2
−
10
x
≤
−
10
y
⇒
x
≥
y
. . . (2)
Solving (1) and (2)
⇒
(
x
−
1
)
2
+
x
2
=
1
⇒
2
x
2
−
2
x
=
0
⇒
x
(
x
−
1
)
=
0
⇒
x
=
0
or
x
=
1
y
=
0
or
y
=
1
Given
x
,
y
∈
I
Points
(
0
,
0
)
,
(
1
,
0
)
,
(
2
,
0
)
,
(
1
,
1
)
,
(
1
,
−
1
)
to find
|
z
1
|
2
+
|
z
2
|
2
+
|
z
3
|
2
+
|
z
4
|
2
+
|
z
5
|
2
=
0
+
1
+
4
+
1
+
1
+
1
+
1
=
9
© examsnet.com
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