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

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

Complex Numbers

H2 Math

International Baccalaureate Higher Level Mathematics

Special Results involving Exponential Forms Q5

Special Results involving Exponential Forms Q5

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