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Test Index
JEE Main Math Class 11 Complex Numbers and Quadratic Equations 2 Questions
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© examsnet.com
Question : 1
Total: 100
Let
Z
1
and
Z
2
be two complex numbers such that
arg
(
Z
1
−
Z
2
)
=
π
4
and
Z
1
,
Z
2
satisfy the equation
|
Z
−
3
|
=
R
e
(
Z
)
. Then, the imaginary part of
Z
1
+
Z
2
is equal to
[2021, 27 Aug. Shift-11]
Your Answer:
Validate
Solution:
Let
Z
1
=
a
1
+
i
b
1
,
Z
2
=
a
2
+
i
b
2
Z
1
−
Z
2
=
(
a
1
−
a
2
)
+
i
(
b
1
−
b
2
)
arg
(
Z
1
−
Z
2
)
=
π
4
⇒
tan
−
1
(
b
1
−
b
2
a
1
−
a
2
)
=
π
4
l
l
⇒
b
1
−
b
2
=
a
1
−
a
2
Also,
|
Z
1
−
3
|
=
R
e
(
Z
1
)
⇒
(
a
1
−
3
)
2
+
b
1
2
=
a
1
2
and
|
Z
2
−
3
|
=
R
e
(
Z
2
)
⇒
(
a
2
−
3
)
2
+
b
2
2
=
a
2
2
⇒
(
a
1
−
3
)
2
−
(
a
2
−
3
)
2
+
b
1
2
−
b
2
2
=
a
1
2
−
a
2
2
⇒
(
a
1
−
a
2
)
(
a
1
+
a
2
−
6
)
+
(
b
1
−
b
2
)
(
b
1
+
b
2
)
=
(
a
1
−
a
2
)
(
a
1
+
a
2
)
⇒
a
1
+
a
2
−
6
+
b
1
+
b
2
=
a
1
+
a
2
⇒
b
1
+
b
2
=
6
⇒
l
m
(
Z
1
+
Z
2
)
=
6
[using Eq. (i).]
© examsnet.com
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