If $ heta=\frac{\pi}{6}$, then the 10th term of $$ \begin{aligned} & 1+(\cos heta+i \sin heta)+(\cos heta+i \sin heta)^2 \ & +(\cos heta+i \sin heta)^3+\ldots ext { is equal to } \end{aligned} $$

Question

If $	heta=\frac{\pi}{6}$, then the 10th term of $$ \begin{aligned} & 1+(\cos 	heta+i \sin 	heta)+(\cos 	heta+i \sin 	heta)^2 \ & +(\cos 	heta+i \sin 	heta)^3+\ldots 	ext { is equal to } \end{aligned} $$

Aicharya · Accepted Answer

$\begin{aligned} T_{10}=(\cos 	heta+i & \sin 	heta)^9 \ & =e^{i 9 	heta}=e^{i 9 \frac{\pi}{6}}=e^{i 3} \frac{\pi}{2}=-i\end{aligned}$

If $\theta=\frac{\pi}{6}$, then the 10th term of $$ \begin{aligned} & 1+(\cos \theta+i \sin \theta)+(\cos…

Solution