Show that $e^{i heta}-e^{-i heta}$ is an imaginary number for all $ heta$. The complex number $w$

Question

Show that $e^{i	heta}-e^{-i	heta}$ is an imaginary number for all $	heta$. The complex number $w$ is given by $w=\dfrac{2}{1-e^{i2	heta}}$, where $0<	heta<\pi$. Show that $\mathrm{Im}(w)=\cot	heta$.

Accepted Answer

$ \text{Im}(w) = \cot\theta $

Special Results involving Exponential Forms Q5

Special Results involving Exponential Forms Q5

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