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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 4 Questions
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© examsnet.com
Question : 2
Total: 37
The area (in sq. units) of the region
S
=
{
z
∈
C
;
|
z
−
1
|
≤
2
;
(
z
+
z
)
+
i
(
z
−
z
)
≤
2
,
lm
(
z
)
≥
0
}
is
[4 Apr 2024 Shift 2]
7
π
3
3
π
2
17
π
8
7
π
4
Validate
Solution:
👈: Video Solution
Put
z
=
x
+
iy
|
z
−
1
|
≤
2
⇒
(
x
−
1
)
2
+
y
2
≤
4
(
z
+
z
)
+
i
(
z
−
z
)
≤
2
⇒
2
x
+
i
(
2
i
y
)
≤
2
⇒
x
−
y
≤
1
.
.
.
(
2
)
Im
(
z
)
≥
0
⇒
y
≥
0
Required area
=
Area of semi-circle
−
area of sector A
1
2
π
(
2
)
2
−
π
2
=
3
π
2
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