Complex Numbers And Quadratic Equations question 391
Question: The value of $ \frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1= $
Options:
A) $ -1 $
B) - 2
C) $ -3 $
D) - 4
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{i^{584}(i^{8}+i^{6}+i^{4}+i^{2}+1)}{i^{574}(i^{8}+i^{6}+i^{4}+i^{2}+1)}-1=\frac{i^{584}}{i^{574}}-1 $ $ =i^{10}-1=-1-1=-2 $
BETA
