Waste less time on Facebook — follow Brilliant.
×

Simple Complex numbers

\[ \large \dfrac2{1 - e^{i \pi /5}} = \dfrac{e^{i \cdot 2\pi /5}}{\sin \frac\pi{10}} \]

Prove the equation above.

Note by TheKiz Zer
9 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

\[e^{\frac{i\pi}{5}}=\cos \frac{\pi}{5}+i\sin \frac{\pi}{5}\\ 1-\cos \frac{\pi}{5}=2\sin^2\frac{\pi}{10}\\ \sin \frac{\pi}{5}=2\sin \frac{\pi}{10}\cos \frac{\pi}{10}\] such that given expression simplifies to:- \[\dfrac{1}{\sin \frac{\pi}{10}(\cos (\frac{-2\pi}{5})+i\sin (\frac{-2\pi}{5}))}\] \[\large =\dfrac{e^{i \cdot 2\pi /5}}{\sin \frac\pi{10}} \] Rishabh Cool · 9 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...