Complex Numbers 1 Question 8
8. The value of
(a)
(b)
(c)
(d) 0
(1998, 2M)
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Answer:
Correct Answer: 8. (b)
Solution:
Alternate Solution
Since, sum of any four consecutive powers of iota is zero.
$$ \begin{aligned} \therefore \sum _{n=1}^{13}\left(i^{n}+i^{n+1}\right) & =\left(i+i^{2}+\ldots+i^{13}\right) \
- & \left(i^{2}+i^{3}+\ldots+i^{14}\right)=i+i^{2}=i-1 \end{aligned} $$
