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AIEEE 2004 Math Solved Paper
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© examsnet.com
Question : 5
Total: 68
If
z
=
x
−
i
y
and
z
1
3
=
p
+
i
q
, then
(
x
p
+
y
q
)
(
p
2
+
q
2
)
is equal to
−
2
−
1
2
1
Validate
Solution:
Given
z
1
3
=
p
+
i
q
⇒
z
=
(
p
+
i
q
)
3
=
p
3
+
(
i
q
)
3
+
3
p
(
i
q
)
(
p
+
i
q
)
=
p
3
−
i
q
3
+
3
i
p
2
q
−
3
p
q
2
=
p
(
p
2
−
3
q
2
)
−
i
q
(
q
2
−
3
p
2
)
Given that
z
=
x
−
i
y
∴
x
−
i
y
=
p
(
p
2
−
3
q
2
)
−
i
q
(
q
2
−
3
p
2
)
By comparing both sides we get,
x
p
=
p
2
−
3
q
2
and
y
q
=
q
2
−
3
p
2
∴
(
2
p
+
y
q
)
(
p
2
+
q
2
)
=
p
2
−
3
q
2
+
q
2
−
3
p
2
p
2
+
q
2
=
−
2
q
2
−
2
p
2
p
2
+
q
2
=
−
2
(
q
2
+
p
2
)
p
2
+
q
2
=
−
2
© examsnet.com
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