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AIEEE 2004 Math Solved Paper
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© examsnet.com
Question : 4
Total: 68
Let
z
and
w
be complex numbers such that
z
+
i
w
=
0
and
arg
z
w
=
π
. Then arg
z
equals
5
π
4
π
2
3
π
4
π
4
Validate
Solution:
Given
z
+
i
w
=
0
⇒
z
=
−
i
w
⇒
z
=
−
i
w
⇒
z
=
−
i
w
⇒
z
=
−
i
w
⇒
z
=
−
(
−
i
)
w
⇒
z
=
i
w
Now given that
Arg
(
zW
)
=
π
⇒
Arg
(
Z
×
z
i
)
=
π
⇒
Arg
(
z
2
)
−
Arg
(
i
)
=
π
⇒
2
Arg
(
z
)
−
π
2
=
π
[
i
complex number represent
(
0
,
1
)
point on imaginary axis and
Arg
(
i
)
means the angle made by the point
(
0
,
1
)
with real axis which is
π
2
]
⇒
2
Arg
(
z
)
=
3
π
2
⇒
Arg
(
z
)
=
3
π
4
© examsnet.com
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