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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 3
Total: 71
If
z
1
and
z
2
are two non-zero complex numbers such that
|
z
1
+
z
2
|
=
|
z
1
|
+
|
z
2
|
, then
arg
z
1
−
arg
z
2
is equal to
π
2
−
π
0
−
π
2
Validate
Solution:
Given that,
|
z
1
+
z
2
|
=
|
z
1
|
+
|
z
2
|
|
z
1
+
z
2
|
is the vector sum of
z
1
and
z
2
. So
|
z
1
+
z
2
|
should be
<
|
z
1
|
+
|
z
2
|
but here they are equal so
z
1
and
z
2
are collinear.
S if
z
1
makes an angle
θ
with
x
axis then
z
2
will also make
θ
angle.
∴
arg
z
1
−
arg
z
2
=
θ
−
θ
=
0
© examsnet.com
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