Just wondering, how does $\displaystyle e^{-z} - e^{z} = 1 - e^{iz}$

My tutor did this, but I'm not sure how he did it.

Thanks.

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- Apr 30th 2011, 06:45 AMGlitchQuick question regarding complex exponentials
Just wondering, how does $\displaystyle e^{-z} - e^{z} = 1 - e^{iz}$

My tutor did this, but I'm not sure how he did it.

Thanks. - Apr 30th 2011, 07:08 AMPlato
- Apr 30th 2011, 07:22 AMGlitch
It came from this:

$\displaystyle \frac{(e^{-z} - e^{z})}{i(e^{-z} + e^{z})} = 2i$

I'm trying to simplify it. - Apr 30th 2011, 07:35 AMPlato
- Apr 30th 2011, 07:42 AMGlitch
Well the question this involves is:

Find all solutions $\displaystyle z \in C$ for $\displaystyle tan(iz) = 2i$

So I used the exponential form of sin and cos to try and get an expression for tan. - Apr 30th 2011, 01:10 PMPlato
- Apr 30th 2011, 07:09 PMGlitch