1. Tardigrade
  2. Question
  3. Mathematics
  4. The smallest positive integer n for which ( (1+i/1-i) )n=1 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The smallest positive integer n for which $ {{\left( \frac{1+i}{1-i} \right)}^{n}}=1 $ is

JamiaJamia 2006

Solution:

Now, $ \frac{1+i}{1-i}=\frac{(1+i)(1+i)}{(1-i)(1+i)}=\frac{1+{{i}^{2}}+2i}{2}=i $ Now, $ {{\left( \frac{1+i}{1-i} \right)}^{n}}=1 $ $ \Rightarrow $ $ {{(i)}^{n}}=1 $ ???(i) $ \Rightarrow $ Least value of n for which Eq. (i) is true is 4 $ \because $ $ {{(i)}^{4}}=1 $