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Byju's Answer
Standard XII
Mathematics
Modulus of a Complex Number
For z being...
Question
For
z
being complex number prove that
|
e
z
|
≤
e
|
z
|
.
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Solution
For
x
,
y
being real numbers we have,
|
x
|
≤
√
x
2
+
y
2
.
We always have,
x
≤
|
x
|
.
Since
e
x
is an increasing function then we get,
e
x
≤
e
|
x
|
≤
e
√
x
2
+
y
2
.
or,
|
e
z
|
≤
e
|
z
|
. [ Since
|
e
z
|
=
e
x
].
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Standard XII Mathematics
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