Complex Numbers And Quadratic Equations question 397
Question: The least positive integer $ n $ which will reduce $ {{( \frac{i-1}{i+1} )}^{n}} $ to a real number, is [Roorkee 1998]
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{( \frac{i-1}{i+1}\times \frac{i-1}{i-1} )}^{n}}={{( \frac{-2i}{-2} )}^{n}}=i^{n} $ Hence, to make the real number the least positive integer is 2.
BETA
