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As it is well known: $$|\sin(x)|\leq |x| \forall x \in \mathbb{R}.$$

Now, if we have a complex number $z$; can I preserve the same inequality

$$|\sin(z)|\leq |z|\quad \forall z \in \mathbb{C}?$$

  • 5
    Think about the purely imaginary case.2012-06-22
  • 1
    [Very related...](http://math.stackexchange.com/questions/142035)2012-06-27

4 Answers 4