# Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1

The following formula holds for $0<|z|<1$: $$\dfrac{|z|}{4} < |e^z-1| < \dfrac{7|z|}{4},$$ where $e^z$ denotes the exponential.