Complex Numbers And Quadratic Equations question 387
Question: If $ {{( \frac{1+i}{1-i} )}^{m}}=1, $ then the least integral value of $ m $ is [IIT 1982; MNR 1984; UPSEAT 2001; MP PET 2002]
Options:
A) 2
B) 4
C) 8
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{1+i}{1-i}=\frac{1+i}{1-i}\times \frac{1+i}{1+i}=\frac{{{(1+i)}^{2}}}{2}=\frac{2i}{2}=i $
$ \therefore $ $ {{( \frac{1+i}{1-i} )}^{m}}=i^{m}=1 $ (as given) So the least value of $ m=4 $ $ {\because i^{4}=1} $
BETA
