Complex Numbers And Quadratic Equations question 404
Question: If $ i^{2}=-1 $ , then sum $ i+i^{2}+i^{3}+… $ to 1000 terms is equal to [Kerala (Engg.) 2002]
Options:
A) 1
B) - 1
C) i
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
$ i+i^{2}+i^{3}+……. $ up to 1000 terms $ =\frac{i(1-i^{1000})}{1-i}= $ $ \frac{i(1-{{(i^{4})}^{250}})}{1-i} $ $ =\frac{i(1-1)}{1-i}=0 $ .
BETA
