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let-z-x-iy-with-x-0-prove-that-e-z-1-z-e-x-1-x-




Question Number 33307 by abdo imad last updated on 14/Apr/18
let z=x+iy  with x≠0 prove?that  ∣ ((e^z  −1)/z) ∣≤∣ ((e^x  −1)/x) ∣
$${let}\:{z}={x}+{iy}\:\:{with}\:{x}\neq\mathrm{0}\:{prove}?{that} \\ $$$$\mid\:\frac{{e}^{{z}} \:−\mathrm{1}}{{z}}\:\mid\leqslant\mid\:\frac{{e}^{{x}} \:−\mathrm{1}}{{x}}\:\mid \\ $$

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