View source for Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))

==Theorem==
The following formula holds for all $z \in \mathbb{C}$:
$$\left| e^z - 1 \right| \leq e^{|z|}-1 \leq |z| e^{|z|},$$
where $e^z$ denotes the [[exponential]].
==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1|next=findme}}: 4.2.39

[[Category:Theorem]]
[[Category:Unproven]]