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AIEEE 2009 Solved Paper
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© examsnet.com
Question : 62
Total: 89
If
|
z
−
4
z
|
=
2
, then the maximum value of
|
z
|
is equal to:
√
5
+
1
2
2
+
√
2
√
3
+
1
Validate
Solution:
Given that
|
z
−
4
z
|
=
2
Now
|
z
|
=
|
z
−
4
z
+
4
−
z
|
≤
|
z
−
4
z
|
+
4
|
z
|
⇒
|
z
|
≤
2
+
4
|
z
|
⇒
|
z
|
2
−
2
|
z
|
−
4
≤
0
⇒
(
|
z
|
−
2
+
√
20
2
)
(
|
z
|
−
2
−
√
20
2
)
≤
0
(
|
z
|
−
(
1
+
√
5
)
)
(
|
z
|
−
(
1
−
√
5
)
)
≤
0
⇒
(
−
√
5
+
1
)
≤
|
z
|
≤
(
√
5
+
1
)
⇒
|
z
|
max
=
√
5
+
1
© examsnet.com
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