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If $\theta=\frac{\pi}{6}$, then the 10th term of
$$
\begin{aligned}
& 1+(\cos \theta+i \sin \theta)+(\cos \theta+i \sin \theta)^2 \\
& +(\cos \theta+i \sin \theta)^3+\ldots \text { is equal to }
\end{aligned}
$$
Options:
$$
\begin{aligned}
& 1+(\cos \theta+i \sin \theta)+(\cos \theta+i \sin \theta)^2 \\
& +(\cos \theta+i \sin \theta)^3+\ldots \text { is equal to }
\end{aligned}
$$
Solution:
2638 Upvotes
Verified Answer
The correct answer is:
$-i$
$\begin{aligned} T_{10}=(\cos \theta+i & \sin \theta)^9 \\ & =e^{i 9 \theta}=e^{i 9 \frac{\pi}{6}}=e^{i 3} \frac{\pi}{2}=-i\end{aligned}$
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