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Byju's Answer
Standard XII
Mathematics
Logarithm of a Complex Number
If z is any...
Question
If
z
is any complex number such that
|
z
+
4
|
≤
3
, then find the greatest value of
|
z
+
1
|
.
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Solution
|
z
+
1
|
=
|
z
+
4
−
3
|
=
|
(
z
+
4
)
+
(
−
3
)
|
≤
|
z
+
4
|
+
|
−
3
|
=
|
z
+
4
|
+
3
≤
3
+
3
=
6
[
∴
|
z
+
4
|
≤
3
]
Hence, the greatest value of
|
z
+
1
|
is 6.
Ans: 6
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