Complex Numbers And Quadratic Equations question 386
Question: If $ n $ is a positive integer, then $ {{( \frac{1+i}{1-i} )}^{4n+1}} $ =
Options:
A) 1
B) - 1
C) $ i $
D) $ -i $
Show Answer
Answer:
Correct Answer: C
Solution:
Since $ \frac{1+i}{1-i}=\frac{(1+i)(1+i)}{(1-i)(1+i)}=i $ Therefore $ {{( \frac{1+i}{1-i} )}^{4n+1}}={i^{4n+1}}=ii^{4n}=i(\because i^{4n}=1) $
BETA
