hello, can you give some hints to prove the following: |1-exp(i theta)|>=2|theta|/pi whenever -pi<=theta<=pi thank you in advance
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i had read some latex tutors on this forum and this is the inequality above: $\displaystyle \forall -\pi\leq\theta\leq\pi : |1-\exp(i \theta)|\geq \frac{2 |\theta|}{\pi}$
Recall Euler's formula: $\displaystyle e^{i\theta}=cos(\theta)+isin(\theta)$ And: $\displaystyle |1- cos(\theta)-isin(\theta)|= (1-cos(\theta))^2+sin^2(\theta)$
Last edited by Also sprach Zarathustra; Jul 18th 2010 at 10:02 AM.
ok, i could arrive at: $\displaystyle |1-e^{i\theta}|=2|sin(\frac{\theta}{2})|$ but how can i extract the term $\displaystyle \frac{\theta}{\pi}$ from the above equation?
Last edited by elfizia2001; Jul 23rd 2010 at 09:16 AM.
hello, please any ideas to solve the above problem?
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