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JEE Advanced 2020 Full Test 4 Paper 1
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© examsnet.com
Question : 50
Total: 54
If
|
z
−
3
|
=
R
e
z
,
|
w
−
3
|
=
R
e
w
and
arg
(
z
−
w
)
=
π
4
,
then find the value of
l
m
(
z
+
w
)
Your Answer:
Validate
Solution:
Let
z
=
x
1
+
i
y
1
,
w
=
x
2
+
i
y
2
∴
|
z
−
3
|
=
R
e
z
⇒
(
x
1
−
3
)
2
+
y
1
2
=
x
1
2
.........(i)
|
w
−
3
|
=
R
e
w
⇒
(
x
2
−
3
)
2
+
y
2
2
=
x
2
2
.........(ii)
arg
(
z
−
w
)
=
π
4
⇒
y
1
−
y
2
x
1
−
x
2
=
tan
π
4
=
1
........(iii)
By solving (i), (ii) and (iii) we get
⇒
y
1
−
y
2
x
1
−
x
2
=
6
y
1
+
y
2
From (iii)
y
1
+
y
2
=
6
© examsnet.com
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